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Journal articles on the topic 'Cyclic groups and regular polygons'

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Published: 4 June 2021

Last updated: 31 January 2023

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1

Rehman, Shafiq Ur, Ghulam Farid, Tayaba Tariq, and Ebenezer Bonyah. "Equal-Square Graphs Associated with Finite Groups." Journal of Mathematics 2022 (February 24, 2022): 1–6. http://dx.doi.org/10.1155/2022/9244325.

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The graphical representation of finite groups is studied in this paper. For each finite group, a simple graph is associated for which the vertex set contains elements of group such that two distinct vertices x and y are adjacent iff x 2 = y 2 . We call this graph an equal-square graph of the finite group G , symbolized by E S G . Some interesting properties of E S G are studied. Moreover, examples of equal-square graphs of finite cyclic groups, groups of plane symmetries of regular polygons, group of units U n , and the finite abelian groups are constructed.

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2

Mullen, Gary L., and Harald Niederreiter. "The structure of a group of permutation polynomials." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 38, no. 2 (April 1985): 164–70. http://dx.doi.org/10.1017/s1446788700023016.

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AbstractLet Gq be the group of permutations of the finite field Fq of odd order q that can be represented by polynomials of the form ax(q+1)/2 + bx with a, b ∈ Fq. It is shown that Gq is isomorphic to the regular wreath product of two cyclic groups. The structure of Gq can also be described in terms of cyclic, dicyclic, and dihedral groups. It also turns out that Gq is isomorphic to the dymmetry group of a regular complex polygon.

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3

Nurfarah Zulkifli and Nor Muhainiah Mohd Ali. "RELATIVE COPRIME PROBABILITY FOR CYCLIC SUBGROUPS OF SOME DIHEDRAL GROUPS." Open Journal of Science and Technology 3, no. 4 (December 29, 2020): 314–21. http://dx.doi.org/10.31580/ojst.v3i4.1679.

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A dihedral group is a group of symmetries of a regular -sided polygon, in other words, a structured operation that will make n-gon to go back to itself through a solid motion. Many researchers have studied various fields of group theory using dihedral groups and one of them is the study of the coprime probability of a group and it is defined as the probability of a random pair of elements in a group G such that the greatest common divisor of the order of x and y, where x and y are in G, is equal to one. The coprime probability of G is then extended to the relative coprime probability G and it is defined as the probability that two randomly selected elements h from H and g from G where H is a subgroup of a group G such that the greatest common divisor of the order of h and order of g, is equal to one. In this research, the concentration is on the generalization of the relative coprime probability for cyclic subgroups of some dihedral groups.

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4

Donkoh, E. K., S. K. Amponsah, and A. A. Opoku. "Overlap Dimensions in Cyclic Tessellable Regular Polygons." Research Journal of Mathematics and Statistics 7, no. 2 (May 25, 2015): 11–16. http://dx.doi.org/10.19026/rjms.7.5274.

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5

BRUCKSTEIN, ALFRED M., GUILLERMO SAPIRO, and DORON SHAKED. "EVOLUTIONS OF PLANAR POLYGONS." International Journal of Pattern Recognition and Artificial Intelligence 09, no. 06 (December 1995): 991–1014. http://dx.doi.org/10.1142/s0218001495000407.

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Evolutions of closed planar polygons are studied in this work. In the first part of the paper, the general theory of linear polygon evolutions is presented, and two specific problems are analyzed. The first one is a polygonal analog of a novel affine-invariant differential curve evolution, for which the convergence of planar curves to ellipses was proved. In the polygon case, convergence to polygonal approximation of ellipses, polygo nal ellipses, is proven. The second one is related to cyclic pursuit problems, and convergence, either to polygonal ellipses or to polygonal circles, is proven. In the second part, two possible polygonal analogues of the well-known Euclidean curve shortening flow are presented. The models follow from geometric considerations. Experimental results show that an arbitrary initial polygon converges to either regular or irregular polygonal approximations of circles when evolving according to the proposed Euclidean flows.

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6

Chinyere, Ihechukwu, and Gerald Williams. "Generalized polygons and star graphs of cyclic presentations of groups." Journal of Combinatorial Theory, Series A 190 (August 2022): 105638. http://dx.doi.org/10.1016/j.jcta.2022.105638.

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7

Friedenberg, Jay. "The Perceived Beauty of Regular Polygon Tessellations." Symmetry 11, no. 8 (August 2, 2019): 984. http://dx.doi.org/10.3390/sym11080984.

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Beauty judgments for regular polygon tessellations were examined in two experiments. In experiment 1 we tested the three regular and eight semi-regular tilings characterized by a single vertex. In experiment 2 we tested the 20 demi-regular tilings containing two vertices. Observers viewed the tessellations at different random orientations inside a circular aperture and rated them using a numeric 1–7 scale. The data from the first experiment show a peak in preference for tiles with two types of polygons and for five polygons around a vertex. Triangles were liked more than other geometric shapes. The results from the second experiment demonstrate a preference for tessellations with a greater number of different kinds of polygons in the overall pattern and for tiles with the greatest difference in the number of polygons between the two vertices. Ratings were higher for tiles with circular arrangements of elements and lower for those with linear arrangements. Symmetry group p6m was liked the most and groups cmm and pmm were liked the least. Taken as a whole the results suggest a preference for complexity and variety in terms of both vertex qualities and symmetric transformations. Observers were sensitive to both the underlying mathematical properties of the patterns as well as their emergent organization.

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8

Conder, Marston D. E., and Thomas W. Tucker. "Regular Cayley maps for cyclic groups." Transactions of the American Mathematical Society 366, no. 7 (March 3, 2014): 3585–609. http://dx.doi.org/10.1090/s0002-9947-2014-05933-3.

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9

Williams, Gordon. "Petrie Schemes." Canadian Journal of Mathematics 57, no. 4 (August 1, 2005): 844–70. http://dx.doi.org/10.4153/cjm-2005-033-6.

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AbstractPetrie polygons, especially as they arise in the study of regular polytopes and Coxeter groups, have been studied by geometers and group theorists since the early part of the twentieth century. An open question is the determination of which polyhedra possess Petrie polygons that are simple closed curves. The current work explores combinatorial structures in abstract polytopes, called Petrie schemes, that generalize the notion of a Petrie polygon. It is established that all of the regular convex polytopes and honeycombs in Euclidean spaces, as well as all of the Gr¨unbaum–Dress polyhedra, possess Petrie schemes that are not self-intersecting and thus have Petrie polygons that are simple closed curves. Partial results are obtained for several other classes of less symmetric polytopes.

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10

Riedl, Jeffrey M. "Automorphisms of Regular Wreath Product -Groups." International Journal of Mathematics and Mathematical Sciences 2009 (2009): 1–12. http://dx.doi.org/10.1155/2009/245617.

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We present a useful new characterization of the automorphisms of the regular wreath product group of a finite cyclic -group by a finite cyclic -group, for any prime , and we discuss an application. We also present a short new proof, based on representation theory, for determining the order of the automorphism group Aut(), where is the regular wreath product of a finite cyclic -group by an arbitrary finite -group.

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11

Lalvani, Haresh. "Non-periodic Space Structures." International Journal of Space Structures 2, no. 2 (June 1987): 93–108. http://dx.doi.org/10.1177/026635118700200204.

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An interesting class of two- and three-dimensional space structures can be derived from projections of higher-dimensional structures. Regular polygons and regular-faced polyhedra provide the geometry of families of n-stars from which two- and three-dimensional projections of n-dimensional grids can be derived. These projections are rhombic space grids composed of all-space filling rhombi and rhombohedra with edges parallel to n directions. An infinite class of single-, double- and multi-layered grids can be derived from n-sided polygons and prisms, and a finite class of multi-directional grids from the polyhedral symmetry groups. The grids can be periodic, centrally symmetric or non-periodic, and act as skeletons to generate corresponding classes of space-filling, packings and labyrinths.

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12

Mousavi, S. Sh, V. Leoreanu-Fotea, and M. Jafarpour. "Cyclic Groups Obtained as Quotient Hypergroups." Annals of the Alexandru Ioan Cuza University - Mathematics 61, no. 1 (January 1, 2015): 109–22. http://dx.doi.org/10.2478/aicu-2014-0043.

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Abstract We introduce a strongly regular equivalence relation ρ*A on the hypergroup H, such that in a particular case the quotient is a cyclic group. Then by using the notion of ρ*A-parts, we investigate the transitivity condition of ρA. Finally, a characterization of the derived hypergroup Dc(H) has been considered.

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13

Feng, Yan-Quan, Kan Hu, Roman Nedela, Martin Škoviera, and Na-Er Wang. "Complete regular dessins and skew-morphisms of cyclic groups." Ars Mathematica Contemporanea 18, no. 2 (October 21, 2020): 289–307. http://dx.doi.org/10.26493/1855-3974.1748.ebd.

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14

Elashvili, A., and M. Jibladze. "Hermite reciprocity for the regular representations of cyclic groups." Indagationes Mathematicae 9, no. 2 (June 1998): 233–38. http://dx.doi.org/10.1016/s0019-3577(98)80021-9.

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15

Smits, Jos T. S., and Piet G. Vos. "The Perception of Continuous Curves in Dot Stimuli." Perception 16, no. 1 (February 1987): 121–31. http://dx.doi.org/10.1068/p160121.

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Two categorisation experiments are reported in which the perceptual phenomenon that some simple arrays of discrete dots appear as a continuous curve whereas others are perceived as an angular contour or as consisting of separate groups of dots was investigated. Triplets of dots were presented in the first experiment, and complete or incomplete regular dot polygons (ie dots positioned on the vertices of imaginary regular polygons) in the second. In both experiments the perception of a curve versus an angle was determined mainly by the relative orientations of the dots, ie by the angles between successive virtual lines, whereas the lengths of the virtual lines had relatively little influence. In experiment 2 the number of displayed dots was shown to be a second independent factor for perceiving continuity. These results are in agreement with results from experiments on dipole textures discrimination, and suggest the psychological existence and importance of virtual lines in the visual processing of dot stimuli.

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16

Hu, Kan, and Young Soo Kwon. "Reflexible complete regular dessins and antibalanced skew morphisms of cyclic groups." Art of Discrete and Applied Mathematics 3, no. 1 (August 3, 2020): #P1.07. http://dx.doi.org/10.26493/2590-9770.1284.3ad.

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17

Giulietti, Massimo, and Gábor Korchmáros. "On cyclic semi-regular subgroups of certain 2-transitive permutation groups." Discrete Mathematics 310, no. 22 (November 2010): 3058–66. http://dx.doi.org/10.1016/j.disc.2009.01.007.

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18

Wang, Yan, and Rong Quan Feng. "Regular Balanced Cayley Maps for Cyclic, Dihedral and Generalized Quaternion Groups." Acta Mathematica Sinica, English Series 21, no. 4 (December 21, 2004): 773–78. http://dx.doi.org/10.1007/s10114-004-0455-7.

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19

Li, Cai Heng. "Permutation Groups with a Cyclic Regular Subgroup and Arc Transitive Circulants." Journal of Algebraic Combinatorics 21, no. 2 (March 2005): 131–36. http://dx.doi.org/10.1007/s10801-005-6903-3.

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20

Ahmadi, Hadi, and Bijan Taeri. "Finite groups with regular join graph of subgroups." Journal of Algebra and Its Applications 15, no. 09 (August 22, 2016): 1650170. http://dx.doi.org/10.1142/s021949881650170x.

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Let [Formula: see text] be a non-trivial finite group different from a cyclic [Formula: see text]-group. The join graph of [Formula: see text] is a graph whose vertex set is the set of all proper subgroups of [Formula: see text] which are not contained in the Frattini subgroup of [Formula: see text] and two distinct vertices [Formula: see text] and [Formula: see text] are joined by an edge if and only if [Formula: see text]. In this paper we classify finite groups with regular graphs and determine their graphs.

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21

Shamsiev, E. A. "Cubature formulas for a disk that are invariant under groups of transformations of regular polygons into themselves." Computational Mathematics and Mathematical Physics 46, no. 7 (July 2006): 1147–54. http://dx.doi.org/10.1134/s0965542506070050.

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22

Riedl, Jeffrey M. "Automorphisms of Iterated Wreath Product p-Groups." Canadian Mathematical Bulletin 55, no. 2 (June 1, 2012): 390–99. http://dx.doi.org/10.4153/cmb-2011-088-3.

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AbstractWe determine the order of the automorphism group Aut(W) for each member W of an important family of finite p-groups that may be constructed as iterated regular wreath products of cyclic groups. We use a method based on representation theory.

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23

Siemons, Johannes, and Alexandre Zalesskiĭ. "Regular orbits of cyclic subgroups in permutation representations of certain simple groups." Journal of Algebra 256, no. 2 (October 2002): 611–25. http://dx.doi.org/10.1016/s0021-8693(02)00107-2.

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24

Blyth, T. S., and H. J. Silva. "Endomorphism regular Ockham algebras of finite Boolean type." Glasgow Mathematical Journal 39, no. 1 (January 1997): 99–110. http://dx.doi.org/10.1017/s0017089500031967.

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AbstractIf (L; ƒ) is an Ockham algebra with dual space (X; g), then it is known that the semigroup of Ockham endomorphisms on L is (anti-)isomorphic to the semigroup Λ(X; g) of continuous order-preserving mappings on X that commute with g. Here we consider the case where L is a finite boolean lattice and ƒ is a bijection. We begin by determining the size of Λ(X;g), and obtain necessary and sufficient conditions for this semigroup to be regular or orthodox. We also describe its structure when it is a group, or an inverse semigroup that is not a group. In the former case it is a cartesian product of cyclic groups and in the latter a cartesian product of cyclic groups each with a zero adjoined.

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25

Conder, Marston, Primož Potočnik, and Jozef Širáň. "Regular maps with almost Sylow-cyclic automorphism groups, and classification of regular maps with Euler characteristic −p2." Journal of Algebra 324, no. 10 (November 2010): 2620–35. http://dx.doi.org/10.1016/j.jalgebra.2010.07.047.

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26

JAMALI, A. R., and M. VISEH. "ON THE EXISTENCE OF NONINNER AUTOMORPHISMS OF ORDER TWO IN FINITE 2-GROUPS." Bulletin of the Australian Mathematical Society 87, no. 2 (September 17, 2012): 278–87. http://dx.doi.org/10.1017/s0004972712000706.

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AbstractIn this paper we prove that every nonabelian finite 2-group with a cyclic commutator subgroup has a noninner automorphism of order two fixing either Φ(G) or Z(G) elementwise. This, together with a result of Peter Schmid on regular p-groups, extends our result to the class of nonabelian finite p-groups with a cyclic commutator subgroup.

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27

Bello, Muhammed, Nor Muhainiah Mohd Ali, and Nurfarah Zulkifli. "A Systematic Approach to Group Properties Using its Geometric Structure." European Journal of Pure and Applied Mathematics 13, no. 1 (January 31, 2020): 84–95. http://dx.doi.org/10.29020/nybg.ejpam.v13i1.3587.

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The algebraic properties of a group can be explored through the relationship among its elements. In this paper, we define the graph that establishes a systematic relationship among the group elements. Let G be a finite group, the order product prime graph of a group G, is a graph having the elements of G as its vertices and two vertices are adjacent if and only if the product of their order is a prime power. We give the general presentation for the graph on dihedral groups and cyclic groups and classify finite dihedral groups and cyclic groups in terms of the order product prime graphs as one of connected, complete, regular and planar. We also obtained some invariants of the graph such as its diameter, girth,independent number and the clique number. Furthermore, we used thevertex-cut of the graph in determining the nilpotency status of dihedralgroups. The graph on dihedral groups is proven to be regular and complete only if the degree of the corresponding group is even prime power and connected for all prime power degree. It is also proven on cyclic groups to be both regular, complete and connected if the group has prime power order. Additionally, the result turn out to show that any dihedral group whose order product prime graph’s vertex-cut is greater than one is nilpotent. We also show that the order product prime graph is planar only when the degree of the group is three for dihedral groups and less than five for cyclic groups. Our final result shows that the order product prime graphs of any two isomorphic groups are isomophic.

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28

Bello, Muhammed, Nor Muhainiah Mohd Ali, and Nurfarah Zulkifli. "A Systematic Approach to Group Properties Using its Geometric Structure." European Journal of Pure and Applied Mathematics 13, no. 1 (January 31, 2020): 84–95. http://dx.doi.org/10.29020/nybg.ejpam.v1i1.3587.

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The algebraic properties of a group can be explored through the relationship among its elements. In this paper, we define the graph that establishes a systematic relationship among the group elements. Let G be a finite group, the order product prime graph of a group G, is a graph having the elements of G as its vertices and two vertices are adjacent if and only if the product of their order is a prime power. We give the general presentation for the graph on dihedral groups and cyclic groups and classify finite dihedral groups and cyclic groups in terms of the order product prime graphs as one of connected, complete, regular and planar. We also obtained some invariants of the graph such as its diameter, girth,independent number and the clique number. Furthermore, we used thevertex-cut of the graph in determining the nilpotency status of dihedralgroups. The graph on dihedral groups is proven to be regular and complete only if the degree of the corresponding group is even prime power and connected for all prime power degree. It is also proven on cyclic groups to be both regular, complete and connected if the group has prime power order. Additionally, the result turn out to show that any dihedral group whose order product prime graph’s vertex-cut is greater than one is nilpotent. We also show that the order product prime graph is planar only when the degree of the group is three for dihedral groups and less than five for cyclic groups. Our final result shows that the order product prime graphs of any two isomorphic groups are isomophic.

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29

Du, Shaofei, Gareth Jones, Jin Ho Kwak, Roman Nedela, and Martin Škoviera. "2-Groups that factorise as products of cyclic groups, and regular embeddings of complete bipartite graphs." Ars Mathematica Contemporanea 6, no. 1 (July 2, 2012): 155–70. http://dx.doi.org/10.26493/1855-3974.295.270.

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30

Jabara, Enrico. "Fixed Point Free Actions of Groups of Exponent 5." Journal of the Australian Mathematical Society 77, no. 3 (December 2004): 297–304. http://dx.doi.org/10.1017/s1446788700014440.

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AbstractIn this paper we prove that if V is a vector space over a field of positive characteristric p ≠ 5 then any regular subgroup A of exponent 5 of GL(V) is cyclic. As a consequence a conjecture of Gupta and Mazurov is proved to be true.

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31

Riedl, Jeffrey M. "Upper central series for elementary-abelian-over-cyclic regular wreath product p-groups." Journal of Algebra and Its Applications 14, no. 04 (February 2015): 1550044. http://dx.doi.org/10.1142/s0219498815500449.

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We compute the upper central series for the regular wreath product finite group C ≀ E where C is a cyclic p-group and E is an elementary abelian p-group for some prime p. The notion of a pattern subgroup enables us to describe the upper central series in a natural way.

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32

Bryant, Peter J. "Cyclic recurrence in nonlinear unidirectional ocean waves." Journal of Fluid Mechanics 192 (July 1988): 329–37. http://dx.doi.org/10.1017/s0022112088001880.

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A fully nonlinear model is developed for the unidirectional propagation of periodic gravity wave groups in deep water, in which the shape of the group envelopes changes cyclically. It is intended to describe the slow-time evolution of wave groups on the open ocean surface, and to generalize the cyclic recurrence that can occur during the sideband modulation of Stokes waves and Schrödinger wave groups. The weak nonlinear interactions are shown to concentrate the wave energy at the centre of each group at regular intervals, causing the waves there to be of greater height locally in space and time. This is suggested as one mechanism for the local wave breaking that is observed on the open ocean surface. The cyclically recurring wave groups may be interpreted as the limit-cycle stage in a progression from uniform wave groups to chaos on the forced, damped, ocean surface.

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33

Ma, Jicheng. "Arc-transitive abelian regular covering graphs." International Journal of Algebra and Computation 26, no. 07 (November 2016): 1369–93. http://dx.doi.org/10.1142/s0218196716500594.

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A lot of attention has been paid recently to the construction of symmetric covers of symmetric graphs. After a new approach given by Conder and the author [Arc-transitive abelian regular covers of cubic graphs, J. Algebra 387 (2013) 215–242], the group of covering transformations can be extended to more general abelian groups rather than cyclic or elementary abelian groups. In this paper, by using the Conder–Ma approach, we investigate the symmetric covers of 4-valent symmetric graphs. As an application, all the arc-transitive abelian regular covers of the 4-valent complete graph [Formula: see text] which can be obtained by lifting the arc-transitive subgroups of automorphisms [Formula: see text] and [Formula: see text] are classified.

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34

IZQUIERDO, MILAGROS, and DANIEL YING. "EQUISYMMETRIC STRATA OF THE MODULI SPACE OF CYCLIC TRIGONAL RIEMANN SURFACES OF GENUS 4." Glasgow Mathematical Journal 51, no. 1 (January 2009): 19–29. http://dx.doi.org/10.1017/s0017089508004497.

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AbstractA closed Riemann surface which can be realized as a three-sheeted covering of the Riemann sphere is called trigonal, and such a covering is called a trigonal morphism. If the trigonal morphism is a cyclic regular covering, the Riemann surface is called a cyclic trigonal Riemann surface. Using the characterization of cyclic trigonality by Fuchsian groups, we find the structure of the space of cyclic trigonal Riemann surfaces of genus 4.

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35

WILDON, MARK. "Permutation groups containing a regular abelian subgroup: the tangled history of two mistakes of Burnside." Mathematical Proceedings of the Cambridge Philosophical Society 168, no. 3 (May 27, 2019): 613–33. http://dx.doi.org/10.1017/s0305004119000033.

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AbstractA group K is said to be a B-group if every permutation group containing K as a regular subgroup is either imprimitive or 2-transitive. In the second edition of his influential textbook on finite groups, Burnside published a proof that cyclic groups of composite prime-power degree are B-groups. Ten years later, in 1921, he published a proof that every abelian group of composite degree is a B-group. Both proofs are character-theoretic and both have serious flaws. Indeed, the second result is false. In this paper we explain these flaws and prove that every cyclic group of composite order is a B-group, using only Burnside’s character-theoretic methods. We also survey the related literature, prove some new results on B-groups of prime-power order, state two related open problems and present some new computational data.

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36

Alspach, Brian, and Shaofei Du. "Suborbit Structure of Permutation p-Groups and an Application to Cayley Digraph Isomorphism." Canadian Mathematical Bulletin 47, no. 2 (June 1, 2004): 161–67. http://dx.doi.org/10.4153/cmb-2004-017-9.

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AbstractLet P be a transitive permutation group of order pm, p an odd prime, containing a regular cyclic subgroup. The main result of this paper is a determination of the suborbits of P. The main result is used to give a simple proof of a recent result by J. Morris on Cayley digraph isomorphisms.

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37

Danchev, Peter V. "A note on nil-clean rings." Acta Universitatis Sapientiae, Mathematica 12, no. 2 (November 1, 2020): 287–93. http://dx.doi.org/10.2478/ausm-2020-0020.

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AbstractWe study a special kind of nil-clean rings, namely those nil-clean rings whose nilpotent elements are difference of two “left-right symmetric” idempotents, and prove that in some various cases they are strongly π-regular. We also show that all nil-clean rings having cyclic unit 2-groups are themselves strongly nil-clean of characteristic 2 (and thus they are again strongly π-regular).

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38

Liu, Jian-Bing, Jaeun Lee, and Jin Ho Kwak. "Enumerating regular graph coverings whose covering transformation groups are ℤ_2-extensions of a cyclic group." Ars Mathematica Contemporanea 15, no. 1 (June 20, 2018): 205–23. http://dx.doi.org/10.26493/1855-3974.1419.3e9.

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39

Kisilevsky, Hershy, and Jack Sonn. "On the minimal ramification problem for ℓ-groups." Compositio Mathematica 146, no. 3 (March 18, 2010): 599–606. http://dx.doi.org/10.1112/s0010437x10004719.

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AbstractLet ℓ be a prime number. It is not known whether every finite ℓ-group of rank n≥1 can be realized as a Galois group over ${\Bbb Q}$ with no more than n ramified primes. We prove that this can be done for the (minimal) family of finite ℓ-groups which contains all the cyclic groups of ℓ-power order and is closed under direct products, (regular) wreath products and rank-preserving homomorphic images. This family contains the Sylow ℓ-subgroups of the symmetric groups and of the classical groups over finite fields of characteristic not ℓ. On the other hand, it does not contain all finite ℓ-groups.

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40

Kongkiatkamon, Suchada, and Chaimongkon Peampring. "Comparison of Regular and Speed Sintering on Low-Temperature Degradation and Fatigue Resistance of Translucent Zirconia Crowns for Implants: An In Vitro Study." Journal of Functional Biomaterials 13, no. 4 (December 8, 2022): 281. http://dx.doi.org/10.3390/jfb13040281.

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Background: Although there are a few studies which compare fast and slow sintering in normal zirconia crowns, it is essential to compare the cracks and load-bearing capacity in zirconia screw-retained implant crowns between regular and speed sintering protocols. This research aimed to compare the surface structure, cracks, and load-bearing capacity in zirconia screw-retained implant crowns between regular sintering (RS) and speed sintering (SS) protocol with and without cyclic loading (fatigue). Methods: A total of 60 screw-retained crowns were fabricated from zirconia (Katana STML Block) by the CAD/CAM system. Then, 30 crowns were subjected to the RS protocol and 30 crowns were subjected to the SS protocol. Cyclic loading was done in half zirconia crowns (15 crowns in each group) using a chewing simulator CS-4.8/CS-4.4 at room temperature. The loading force was applied on the middle of the crowns by a metal stylus underwater at room temperature with a chewing simulator at an axial 50 N load for 240,000 cycles and lateral movement at 2 mm. Scanning electron microscopy was done to study the surface of the crowns and the cracks in the crowns of the regular and speed sintering protocols, with and without fatigue. Results: For the speed sintering group, the surface looks more uniform, and the crack lines are present at a short distance compared to regular sintering. The sintering protocol with a larger Weibull module and durability increases the reliability. It showed that the Speed group showed the maximum fracture load, followed by the regular, speed fatigue, and regular fatigue groups. The fracture load in various groups showed significant differences. Conclusions: It was found that the speed group showed the maximum fracture load followed by the regular, speed fatigue, and regular fatigue. The crack lines ran from occlusal to bottoms (gingiva) and the arrest lines were perpendicular to the crack propagations.

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41

Kwak, Jin Ho, and Ju Mok Oh. "One–regular Normal Cayley Graphs on Dihedral Groups of Valency 4 or 6 with Cyclic Vertex Stabilizer." Acta Mathematica Sinica, English Series 22, no. 5 (April 26, 2006): 1305–20. http://dx.doi.org/10.1007/s10114-005-0752-9.

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Costa, Antonio F., and Milagros Izquierdo. "On real trigonal Riemann surfaces." MATHEMATICA SCANDINAVICA 98, no. 1 (March 1, 2006): 53. http://dx.doi.org/10.7146/math.scand.a-14983.

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A closed Riemann surface $X$ which can be realized as a 3-sheeted covering of the Riemann sphere is called trigonal, and such a covering will be called a trigonal morphism. A trigonal Riemann surface $X$ is called real trigonal if there is an anticonformal involution (symmetry) $\sigma$ of $X$ commuting with the trigonal morphism. If the trigonal morphism is a cyclic regular covering the Riemann surface is called real cyclic trigonal. The species of the symmetry $\sigma $ is the number of connected components of the fixed point set $\mathrm{Fix}(\sigma)$ and the orientability of the Klein surface $X/\langle\sigma\rangle$. We characterize real trigonality by means of Fuchsian and NEC groups. Using this approach we obtain all possible species for the symmetry of real cyclic trigonal and real non-cyclic trigonal Riemann surfaces.

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43

Westlund, Erik E. "Hamilton decompositions of certain 6-regular Cayley graphs on Abelian groups with a cyclic subgroup of index two." Discrete Mathematics 312, no. 22 (November 2012): 3228–35. http://dx.doi.org/10.1016/j.disc.2012.07.017.

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Anna V., Martsinkevich. "Quasinormal Fitting classes of finite groups." Journal of the Belarusian State University. Mathematics and Informatics, no. 2 (August 1, 2019): 18–26. http://dx.doi.org/10.33581/2520-6508-2019-2-18-26.

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Let P be the set of all primes, Zn a cyclic group of order n and X wr Zn the regular wreath product of the group X with Zn. A Fitting class F is said to be X-quasinormal (or quasinormal in a class of groups X ) if F ⊆ X, p is a prime, groups G ∈ F and G wr Zp ∈ X, then there exists a natural number m such that G m wr Zp ∈ F. If X is the class of all soluble groups, then F is normal Fitting class. In this paper we generalize the well-known theorem of Blessenohl and Gaschütz in the theory of normal Fitting classes. It is proved, that the intersection of any set of nontrivial X-quasinormal Fitting classes is a nontrivial X-quasinormal Fitting class. In particular, there exists the smallest nontrivial X-quasinormal Fitting class. We confirm a generalized version of the Lockett conjecture (in particular, the Lockett conjecture) about the structure of a Fitting class for the case of X-quasinormal classes, where X is a local Fitting class of partially soluble groups.

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Kuhn, Gabriella. "Anisotropic random walks on free products of cyclic groups, irreducible representations and idempotents of C*reg(G)." Nagoya Mathematical Journal 128 (December 1992): 95–120. http://dx.doi.org/10.1017/s0027763000004232.

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Let be the free product of q + 1 copies of Zn+1 and let denote its Cayley graph (with respect to aj, 1 ≤ j ≤ q + 1). We may think of G as a group acting on the “homogeneous space” , This point of view is inspired by the case of SL2(R) acting on the hyperbolic disk and is developed in [FT-P] [I-P] [FT-S] [S] (but see also [C]).Since G is a group we may investigate some classical topics: the full (reductive) C* algebra, its dual space, the regular Von Neumann algebra and so on. See [B] [P] [L] [V] and also [H]. These approaches give results pointing up the analogy between harmonic analysis on these groups and harmonic analysis on more classical objects.

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Naghipour, Avaz, Mohammad Ali Jafarizadeh, and Sedaghat Shahmorad. "Quantum stabilizer codes from Abelian and non-Abelian groups association schemes." International Journal of Quantum Information 13, no. 03 (April 2015): 1550021. http://dx.doi.org/10.1142/s0219749915500215.

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A new method for the construction of the binary quantum stabilizer codes is provided, where the construction is based on Abelian and non-Abelian groups association schemes. The association schemes based on non-Abelian groups are constructed by bases for the regular representation from U6n, T4n, V8n and dihedral D2n groups. By using Abelian group association schemes followed by cyclic groups and non-Abelian group association schemes a list of binary stabilizer codes up to 40 qubits is given in tables 4, 5 and 10. Moreover, several binary stabilizer codes of minimum distances 5, 7 and 8 with good quantum parameters is presented. The preference of this method specially for Abelian group association schemes is that one can construct any binary quantum stabilizer code with any distance by using the commutative structure of association schemes.

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HOLT, DEREK F., SARAH REES, and CLAAS E. RÖVER. "GROUPS WITH CONTEXT-FREE CONJUGACY PROBLEMS." International Journal of Algebra and Computation 21, no. 01n02 (February 2011): 193–216. http://dx.doi.org/10.1142/s0218196711006133.

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The conjugacy problem and the inverse conjugacy problem of a finitely generated group are defined, from a language theoretic point of view, as sets of pairs of words. An automaton might be obliged to read the two input words synchronously, or could have the option to read asynchronously. Hence each class of languages gives rise to four classes of groups; groups whose (inverse) conjugacy problem is an (a)synchronous language in the given class. For regular languages all these classes are identical with the class of finite groups. We show that the finitely generated groups with asynchronously context-free inverse conjugacy problem are precisely the virtually free groups. Moreover, the other three classes arising from context-free languages are shown all to coincide with the class of virtually cyclic groups, which is precisely the class of groups with synchronously one-counter (inverse) conjugacy problem. It is also proved that, for a δ-hyperbolic group and any λ ≥ 1, ϵ ≥ 0, the intersection of the inverse conjugacy problem with the set of pairs of (λ, ϵ)-quasigeodesics is context-free. Finally we show that the conjugacy problem of a virtually free group is an asynchronously indexed language.

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HOELSCHER, JING LONG. "RAY CLASS GROUPS OF QUADRATIC AND CYCLOTOMIC FIELDS." International Journal of Number Theory 06, no. 05 (August 2010): 1169–82. http://dx.doi.org/10.1142/s1793042110003447.

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This paper studies Galois extensions over real quadratic number fields or cyclotomic number fields ramified only at one prime. In both cases, the ray class groups are computed, and they give restrictions on the finite groups that can occur as such Galois groups. Let [Formula: see text] be a real quadratic number field with a prime P lying above p in ℚ. If p splits in K/ℚ and p does not divide the big class number of K, then any pro-p extension of K ramified only at P is finite cyclic. If p is inert in K/ℚ, then there exist infinite extensions of K ramified only at P. Furthermore, for big enough integer k, the ray class field (mod Pk+1) is obtained from the ray class field (mod Pk) by adjoining ζpk+1. In the case of a regular cyclotomic number field K = ℚ(ζp), the explicit structure of ray class groups (mod Pk) is given for any positive integer k, where P is the unique prime in K above p.

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Bello, Muhammed, Nor Muhainiah Mohd Ali, and Surajo Ibrahim Isah. "Graph coloring using commuting order product prime graph." Journal of Mathematics and Computer Science 23, no. 02 (October 24, 2020): 155–69. http://dx.doi.org/10.22436/jmcs.023.02.08.

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The concept of graph coloring has become a very active field of research that enhances many practical applications and theoretical challenges. Various methods have been applied in carrying out this study. Let G be a finite group. In this paper, we introduce a new graph of groups, which is a commuting order product prime graph of finite groups as a graph having the elements of G as its vertices and two vertices are adjacent if and only if they commute and the product of their order is a prime power. This is an extension of the study for order product prime graph of finite groups. The graph's general presentations on dihedral groups, generalized quaternion groups, quasi-dihedral groups, and cyclic groups have been obtained in this paper. Moreover, the commuting order product prime graph on these groups has been classified as connected, complete, regular, or planar. These results are used in studying various and recently introduced chromatic numbers of graphs.

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Bryant, R. M., and I. C. Michos. "Lie powers of free modules for certain groups of prime power order." Journal of the Australian Mathematical Society 71, no. 2 (October 2001): 149–58. http://dx.doi.org/10.1017/s1446788700002792.

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AbstractLet G be a finite group of order pk, where p is a prime and k ≥ 1, such that G is either cyclic, quaternion or generalised quaternion. Let V be a finite-dimensional free KG-module where K is a field of characteristic p. The Lie powers Ln(V) are naturally KG-modules and the main result identifies these modules up to isomorphism. There are only two isomorphism types of indecomposables occurring as direct summands of these modules, namely the regular KG-module and the indecomposable of dimension pk – pk−1 induced from the indecomposable K H-module of dimension p − 1, where H is the unique subgroup of G of order p. Formulae are given for the multiplicities of these indecomposables in Ln(V). This extends and utilises work of the first author and R. Stöhr concerned with the case where G has order p.

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