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Journal articles on the topic 'Finite groups'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 August 2024

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1

A. Jund, Asaad, and Haval M. Mohammed Salih. "Result Involution Graphs of Finite Groups." Journal of Zankoy Sulaimani - Part A 23, no. 1 (June 20, 2021): 113–18. http://dx.doi.org/10.17656/jzs.10846.

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2

Zhang, Jinshan, Zhencai Shen, and Jiangtao Shi. "Finite groups with few vanishing elements." Glasnik Matematicki 49, no. 1 (June 8, 2014): 83–103. http://dx.doi.org/10.3336/gm.49.1.07.

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3

Kondrat'ev, A. S., A. A. Makhnev, and A. I. Starostin. "Finite groups." Journal of Soviet Mathematics 44, no. 3 (February 1989): 237–318. http://dx.doi.org/10.1007/bf01676868.

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4

Andruskiewitsch, N., and G. A. García. "Extensions of Finite Quantum Groups by Finite Groups." Transformation Groups 14, no. 1 (November 18, 2008): 1–27. http://dx.doi.org/10.1007/s00031-008-9039-4.

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5

Conrad, Paul F., and Jorge Martinez. "Locally finite conditions on lattice-ordered groups." Czechoslovak Mathematical Journal 39, no. 3 (1989): 432–44. http://dx.doi.org/10.21136/cmj.1989.102314.

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6

Chen, Yuanqian, Paul Conrad, and Michael Darnel. "Finite-valued subgroups of lattice-ordered groups." Czechoslovak Mathematical Journal 46, no. 3 (1996): 501–12. http://dx.doi.org/10.21136/cmj.1996.127311.

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7

Kniahina, V. N., and V. S. Monakhov. "Finite groups with semi-subnormal Schmidt subgroups." Algebra and Discrete Mathematics 29, no. 1 (2020): 66–73. http://dx.doi.org/10.12958/adm1376.

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8

Cao, Jian Ji, and Xiu Yun Guo. "Finite NPDM-groups." Acta Mathematica Sinica, English Series 37, no. 2 (February 2021): 306–14. http://dx.doi.org/10.1007/s10114-021-8047-3.

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9

Burn, R. P., L. C. Grove, and C. T. Benson. "Finite Reflection Groups." Mathematical Gazette 70, no. 451 (March 1986): 77. http://dx.doi.org/10.2307/3615867.

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10

Stonehewer, S. E. "FINITE SOLUBLE GROUPS." Bulletin of the London Mathematical Society 25, no. 5 (September 1993): 505–6. http://dx.doi.org/10.1112/blms/25.5.505.

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11

MCIVER, ANNABELLE, and PETER M. NEUMANN. "ENUMERATING FINITE GROUPS." Quarterly Journal of Mathematics 38, no. 4 (1987): 473–88. http://dx.doi.org/10.1093/qmath/38.4.473.

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12

Cherlin, Gregory, and Ulrich Felgner. "Homogeneous Finite Groups." Journal of the London Mathematical Society 62, no. 3 (December 2000): 784–94. http://dx.doi.org/10.1112/s0024610700001484.

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13

Blackburn, Norman, Marian Deaconescu, and Avinoam Mann. "Finite equilibrated groups." Mathematical Proceedings of the Cambridge Philosophical Society 120, no. 4 (November 1996): 579–88. http://dx.doi.org/10.1017/s0305004100001560.

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If H, K are subgroups of a group G, then HK is a subgroup of G if and only if HK = KH. This condition certainly holds if H ≤ NG(K) or K ≤ NG(H). But the majority of groups can also be expressed as HK, where neither H nor K is normal. In this paper we consider groups G for which no subgroup G1 can be expressed as the product of non-normal subgroups of G1. Such a group is said to be equilibrated. Thus G is equilibrated if and only if either H ≤ NG(K) or K ≤ NG(H) whenever H, K and HK are subgroups of G.

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14

Heineken, Hermann. "Finite complete groups." Rendiconti del Seminario Matematico e Fisico di Milano 54, no. 1 (December 1985): 29–34. http://dx.doi.org/10.1007/bf02924848.

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15

Starostin, A. I. "Finite p-groups." Journal of Mathematical Sciences 88, no. 4 (February 1998): 559–85. http://dx.doi.org/10.1007/bf02365317.

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16

Myl’nikov, A. L. "Finite tangled groups." Siberian Mathematical Journal 48, no. 2 (March 2007): 295–99. http://dx.doi.org/10.1007/s11202-007-0030-4.

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17

Myasnikov, Alexei, and Denis Osin. "Algorithmically finite groups." Journal of Pure and Applied Algebra 215, no. 11 (November 2011): 2789–96. http://dx.doi.org/10.1016/j.jpaa.2011.03.019.

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18

Huang, Hua-Lin, Yuping Yang, and Yinhuo Zhang. "On nondiagonal finite quasi-quantum groups over finite abelian groups." Selecta Mathematica 24, no. 5 (June 7, 2018): 4197–221. http://dx.doi.org/10.1007/s00029-018-0420-4.

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19

Reid, J. D. "On Finite Groups and Finite Fields." American Mathematical Monthly 98, no. 6 (June 1991): 549. http://dx.doi.org/10.2307/2324878.

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20

WILSON, JOHN S. "FINITE AXIOMATIZATION OF FINITE SOLUBLE GROUPS." Journal of the London Mathematical Society 74, no. 03 (December 2006): 566–82. http://dx.doi.org/10.1112/s0024610706023106.

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21

Lubotzky, Alexander, and Avinoam Mann. "Residually finite groups of finite rank." Mathematical Proceedings of the Cambridge Philosophical Society 106, no. 3 (November 1989): 385–88. http://dx.doi.org/10.1017/s0305004100068110.

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The recent constructions, by Rips and Olshanskii, of infinite groups with all proper subgroups of prime order, and similar ‘monsters’, show that even under the imposition of apparently very strong finiteness conditions, the structure of infinite groups can be rather weird. Thus it seems reasonable to impose the type of condition that enables us to apply the theory of finite groups. Two such conditions are local finiteness and residual finiteness, and here we are interested in the latter. Specifically, we consider residually finite groups of finite rank, where a group is said to have rank r, if all finitely generated subgroups of it can be generated by r elements. Recall that a group is said to be virtually of some property, if it has a subgroup of finite index with this property. We prove the following result:Theorem 1. A residually finite group of finite rank is virtually locally soluble.

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22

Reid, J. D. "On Finite Groups and Finite Fields." American Mathematical Monthly 98, no. 6 (June 1991): 549–51. http://dx.doi.org/10.1080/00029890.1991.11995756.

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23

Wei, X., A. Kh Zhurtov, D. V. Lytkina, and V. D. Mazurov. "Finite groups close to Frobenius groups." Sibirskii matematicheskii zhurnal 60, no. 5 (August 30, 2019): 1035–40. http://dx.doi.org/10.33048/smzh.2019.60.504.

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24

Sozutov, A. I. "Groups Saturated with Finite Frobenius Groups." Mathematical Notes 109, no. 1-2 (January 2021): 270–79. http://dx.doi.org/10.1134/s0001434621010314.

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25

Wei, X., A. Kh Zhurtov, D. V. Lytkina, and V. D. Mazurov. "Finite Groups Close to Frobenius Groups." Siberian Mathematical Journal 60, no. 5 (September 2019): 805–9. http://dx.doi.org/10.1134/s0037446619050045.

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26

Lubotzky, Alexander, and Avinoam Mann. "Powerful p-groups. I. Finite groups." Journal of Algebra 105, no. 2 (February 1987): 484–505. http://dx.doi.org/10.1016/0021-8693(87)90211-0.

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27

Lytkina, D. V. "Groups saturated by finite simple groups." Algebra and Logic 48, no. 5 (September 2009): 357–70. http://dx.doi.org/10.1007/s10469-009-9063-z.

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28

Pettet, Martin R. "Locally finite groups as automorphism groups." Archiv der Mathematik 48, no. 1 (January 1987): 1–9. http://dx.doi.org/10.1007/bf01196346.

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29

Hussain, Muhammad Tanveer, and Shamsher Ullah. "On nearly SΦ-normal subgroups of finite groups." Algebra and Discrete Mathematics 36, no. 2 (2023): 151–65. http://dx.doi.org/10.12958/adm2007.

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30

Li, Changwen. "On weakly s-normal subgroups of finite groups." Algebra and Discrete Mathematics 36, no. 2 (2023): 179–87. http://dx.doi.org/10.12958/adm1673.

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31

Trofimuk, Alexander. "FINITE GROUPS WITH GIVEN SYSTEMS OF PROPERMUTABLE SUBGROUPS." Eurasian Mathematical Journal 15, no. 1 (2024): 91–97. http://dx.doi.org/10.32523/2077-9879-2024-15-1-91-97.

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32

Zimmerman, Jay. "Finite Groups Which are Automorphism Groups of Infinite Groups Only." Canadian Mathematical Bulletin 28, no. 1 (March 1, 1985): 84–90. http://dx.doi.org/10.4153/cmb-1985-008-4.

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AbstractThe object of this paper is to exhibit an infinite set of finite semisimple groups H, each of which is the automorphism group of some infinite group, but of no finite group. We begin the construction by choosing a finite simple group S whose outer automorphism group and Schur multiplier possess certain specified properties. The group H is a certain subgroup of Aut S which contains S. For example, most of the PSL's over a non-prime finite field are candidates for S, and in this case, H is generated by all of the inner, diagonal and graph automorphisms of S.

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33

Bandman, Tatiana, Gert-Martin Greuel, Fritz Grunewald, Boris Kunyavskii, Gerhard Pfister, and Eugene Plotkin. "Identities for finite solvable groups and equations in finite simple groups." Compositio Mathematica 142, no. 03 (May 2006): 734–64. http://dx.doi.org/10.1112/s0010437x0500179x.

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34

Kozhukhov, S. F. "FINITE AUTOMORPHISM GROUPS OF TORSION-FREE ABELIAN GROUPS OF FINITE RANK." Mathematics of the USSR-Izvestiya 32, no. 3 (June 30, 1989): 501–21. http://dx.doi.org/10.1070/im1989v032n03abeh000778.

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35

Durakov, B. E., and A. I. Sozutov. "On Periodic Groups Saturated with Finite Frobenius Groups." Bulletin of Irkutsk State University. Series Mathematics 35 (2021): 73–86. http://dx.doi.org/10.26516/1997-7670.2021.35.73.

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A group is called weakly conjugate biprimitively finite if each its element of prime order generates a finite subgroup with any of its conjugate elements. A binary finite group is a periodic group in which any two elements generate a finite subgroup. If $\mathfrak{X}$ is some set of finite groups, then the group $G$ saturated with groups from the set $\mathfrak{X}$ if any finite subgroup of $G$ is contained in a subgroup of $G$, isomorphic to some group from $\mathfrak{X}$. A group $G = F \leftthreetimes H$ is a Frobenius group with kernel $F$ and a complement $H$ if $H \cap H^f = 1$ for all $f \in F^{\#}$ and each element from $G \setminus F$ belongs to a one conjugated to $H$ subgroup of $G$. In the paper we prove that a saturated with finite Frobenius groups periodic weakly conjugate biprimitive finite group with a nontrivial locally finite radical is a Frobenius group. A number of properties of such groups and their quotient groups by a locally finite radical are found. A similar result was obtained for binary finite groups with the indicated conditions. Examples of periodic non locally finite groups with the properties above are given, and a number of questions on combinatorial group theory are raised.

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36

Borovik, Alexandre, and Ulla Karhumäki. "Locally finite groups of finite centralizer dimension." Journal of Group Theory 22, no. 4 (July 1, 2019): 729–40. http://dx.doi.org/10.1515/jgth-2018-0109.

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37

Zimmermann, Bruno. "Finite groups of outer automorphisms of free groups." Glasgow Mathematical Journal 38, no. 3 (September 1996): 275–82. http://dx.doi.org/10.1017/s0017089500031700.

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Let Fr denote the free group of rank r and Out Fr: = AutFr/Inn Fr the outer automorphism group of Fr (automorphisms modulo inner automorphisms). In [10] we determined the maximal order 2rr! (for r > 2) for finite subgroups of Out Fr as well as the finite subgroup of that order which, for r > 3, is unique up to conjugation. In the present paper we determine all maximal finite subgroups (that is not contained in a larger finite subgroup) of Out F3, up to conjugation (Theorem 2 in Section 3). Here the considered case r = 3 serves as a model case: our method can be applied for other small values of r (in principle for any value of r) but the computations become considerably longer and are more apt for a computer then; the method can also be applied to determine the maximal finite subgroups of the automorphism group Aut Fr of Fr. Note that the canonical projection Aut Fr ⃗ Out Fr is injective on finite subgroups of Aut Fr; however, not all finite subgroups of Out Fr lift to finite subgroups of Aut Fr.

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38

Cheung, K., and M. Mosca. "Decomposing finite Abelian groups." Quantum Information and Computation 1, no. 3 (October 2001): 26–32. http://dx.doi.org/10.26421/qic1.3-2.

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This paper describes a quantum algorithm for efficiently decomposing finite Abelian groups into a product of cyclic groups. Such a decomposition is needed in order to apply the Abelian hidden subgroup algorithm. Such a decomposition (assuming the Generalized Riemann Hypothesis) also leads to an efficient algorithm for computing class numbers (known to be at least as difficult as factoring).

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39

Leavitt, J. L., G. J. Sherman, and M. E. Walker. "Rewriteability in Finite Groups." American Mathematical Monthly 99, no. 5 (May 1992): 446. http://dx.doi.org/10.2307/2325089.

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40

Witbooi, Peter. "Finite images of groups." Quaestiones Mathematicae 23, no. 3 (September 2000): 279–85. http://dx.doi.org/10.2989/16073600009485977.

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41

Gil, Antoni, and José R. Martínez. "Mutations in finite groups." Bulletin of the Belgian Mathematical Society - Simon Stevin 1, no. 4 (1994): 491–506. http://dx.doi.org/10.36045/bbms/1103408606.

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42

Huang, J., B. Hu, and A. N. Skiba. "Finite generalized soluble groups." Algebra i logika 58, no. 2 (July 9, 2019): 252–70. http://dx.doi.org/10.33048/alglog.2019.58.207.

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43

Chuang, Joseph, Markus Linckelmann, Gunter Malle, and Jeremy Rickard. "Representations of Finite Groups." Oberwolfach Reports 9, no. 1 (2012): 963–1019. http://dx.doi.org/10.4171/owr/2012/16.

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44

Chuang, Joseph, Meinolf Geck, Markus Linckelmann, and Gabriel Navarro. "Representations of Finite Groups." Oberwolfach Reports 12, no. 2 (2015): 971–1027. http://dx.doi.org/10.4171/owr/2015/18.

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45

Chuang, Joseph, Meinolf Geck, Radha Kessar, and Gabriel Navarro. "Representations of Finite Groups." Oberwolfach Reports 16, no. 1 (February 26, 2020): 841–95. http://dx.doi.org/10.4171/owr/2019/14.

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46

Sun, Zhi-Wei. "Finite coverings of groups." Fundamenta Mathematicae 134, no. 1 (1990): 37–53. http://dx.doi.org/10.4064/fm-134-1-37-53.

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47

Chupordia, V. A. "On finite-finitary groups." Researches in Mathematics 15 (February 15, 2021): 154. http://dx.doi.org/10.15421/240723.

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48

Broto, Carles, and Jesper Møller. "Chevalleyp–local finite groups." Algebraic & Geometric Topology 7, no. 4 (December 18, 2007): 1809–919. http://dx.doi.org/10.2140/agt.2007.7.1809.

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49

Deaconescu, Marian, and Gary L. Walls. "Finite Groups with Poles." Algebra Colloquium 13, no. 03 (September 2006): 507–12. http://dx.doi.org/10.1142/s1005386706000459.

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50

Attar, M. Shabani. "Semicomplete Finite p-Groups." Algebra Colloquium 18, spec01 (December 2011): 937–44. http://dx.doi.org/10.1142/s1005386711000812.

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Let G be a group and G' be its commutator subgroup. An automorphism α of G is called an IA-automorphism if x-1α (x) ∈ G' for each x ∈ G. The set of all IA-automorphisms of G is denoted by IA (G). A group G is called semicomplete if and only if IA (G)= Inn (G), where Inn (G) is the inner automorphism group of G. In this paper we characterize semicomplete finite p-groups of class 2, give some necessary conditions for finite p-groups to be semicomplete, and characterize semicomplete non-abelian groups of orders p4 and p5.

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