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Journal articles on the topic 'Products of groups'

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Published: 10 March 2023

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1

Frič, Roman. "Products of coarse convergence groups." Czechoslovak Mathematical Journal 38, no. 2 (1988): 285–90. http://dx.doi.org/10.21136/cmj.1988.102224.

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2

S. Alexander, S. Alexander, and Dr R. Selvaraj Dr.R.Selvaraj. "Marketing of Self Help Groups Products." Indian Journal of Applied Research 4, no. 6 (October 1, 2011): 96–99. http://dx.doi.org/10.15373/2249555x/june2014/29.

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3

Adian, S. I., and V. S. Atabekyan. "Periodic products of groups." Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences) 52, no. 3 (May 2017): 111–17. http://dx.doi.org/10.3103/s1068362317030013.

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4

Jones, Julie C. "Products of protopological groups." International Journal of Mathematics and Mathematical Sciences 28, no. 7 (2001): 433–35. http://dx.doi.org/10.1155/s016117120100727x.

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Montgomery and Zippin saied that a group is approximated by Lie groups if every neighborhood of the identity contains an invariant subgroupHsuch thatG/His topologically isomorphic to a Lie group. Bagley, Wu, and Yang gave a similar definition, which they called a pro-Lie group. Covington extended this concept to a protopological group. Covington showed that protopological groups possess many of the characteristics of topological groups. In particular, Covington showed that in a special case, the product of protopological groups is a protopological group. In this note, we give a characterization theorem for protopological groups and use it to generalize her result about products to the category of all protopological groups.
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5

Rychkov, S. V. "Verbal products of groups." Algebra and Logic 32, no. 2 (March 1993): 87–96. http://dx.doi.org/10.1007/bf02260879.

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6

Remeslennikov, V. N., and N. S. Romanovskii. "Metabelian Products of Groups." Algebra and Logic 43, no. 3 (May 2004): 190–97. http://dx.doi.org/10.1023/b:allo.0000028932.26405.a9.

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7

Barry, Michael J. J., and Michael B. Ward. "Products of Sylow groups." Archiv der Mathematik 63, no. 4 (October 1994): 289–90. http://dx.doi.org/10.1007/bf01189562.

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8

Campagnolo, Caterina, and Holger Kammeyer. "Products of free groups in Lie groups." Journal of Algebra 579 (August 2021): 237–55. http://dx.doi.org/10.1016/j.jalgebra.2021.03.023.

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9

Walls, Gary L. "Products of simple groups and symmetric groups." Archiv der Mathematik 58, no. 4 (April 1992): 313–21. http://dx.doi.org/10.1007/bf01189917.

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10

Freslon, Amaury, and Adam Skalski. "Wreath products of finite groups by quantum groups." Journal of Noncommutative Geometry 12, no. 1 (March 23, 2018): 29–68. http://dx.doi.org/10.4171/jncg/270.

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11

Walls, Gary L. "Groups which are products of finite simple groups." Archiv der Mathematik 50, no. 1 (January 1988): 1–4. http://dx.doi.org/10.1007/bf01313486.

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12

Llosa Isenrich, Claudio. "Kähler groups and subdirect products of surface groups." Geometry & Topology 24, no. 2 (September 23, 2020): 971–1017. http://dx.doi.org/10.2140/gt.2020.24.971.

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13

Ciobanu, Laura, Derek F. Holt, and Sarah Rees. "Sofic groups: graph products and graphs of groups." Pacific Journal of Mathematics 271, no. 1 (September 10, 2014): 53–64. http://dx.doi.org/10.2140/pjm.2014.271.53.

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14

Krupiński, Krzysztof. "Products of finite abelian groups as profinite groups." Journal of Algebra 288, no. 2 (June 2005): 556–82. http://dx.doi.org/10.1016/j.jalgebra.2005.01.011.

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15

Wilson, John S. "Soluble groups which are products of minimax groups." Archiv der Mathematik 50, no. 3 (May 1988): 193–98. http://dx.doi.org/10.1007/bf01187732.

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16

Amberg, Bernhard, and Yaroslav Sysak. "Products of locally cyclic groups." Archiv der Mathematik 117, no. 1 (April 16, 2021): 19–28. http://dx.doi.org/10.1007/s00013-021-01593-1.

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AbstractWe consider groups of the form $${G} = {AB}$$ G = AB with two locally cyclic subgroups A and B. The structure of these groups is determined in the cases when A and B are both periodic or when one of them is periodic and the other is not. Together with a previous study of the case where A and B are torsion-free, this gives a complete classification of all groups that are the product of two locally cyclic subgroups. As an application, it is shown that the Prüfer rank of a periodic product of two locally cyclic subgroups does not exceed 3, and this bound is sharp. It is also proved that a product of a finite number of pairwise permutable periodic locally cyclic subgroups is a locally supersoluble group. This generalizes a well-known theorem of B. Huppert for finite groups.
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17

Kotschick, D., and C. Löh. "Groups not presentable by products." Groups, Geometry, and Dynamics 7, no. 1 (2013): 181–204. http://dx.doi.org/10.4171/ggd/180.

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18

Bartholdi, Laurent, and Said Sidki. "Self-similar products of groups." Groups, Geometry, and Dynamics 14, no. 1 (February 27, 2020): 107–15. http://dx.doi.org/10.4171/ggd/536.

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19

Razzaghmaneshi, Behnam. "Supersoluble Groups and Its Products." Journal of Engineering and Applied Sciences Technology 2, no. 2 (June 30, 2020): 1–3. http://dx.doi.org/10.47363/jeast/2020(2)108.

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Two subgroups A and B of a group G are called permutable if every subgroup X of A is permutable with every subgroup Y of B, i.e., XYis a subgroup of G. In this case, if G=AB we say that G is the permutable product of the subgroups A and B. In this paper we check the permutable product of supersoluble subgroups. And the end, we obtain sufficient conditions for permutable products of finite supersoluble groups to be supersoluble.
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20

Liu, Xi, Wenbin Guo, and K. P. Shum. "Products of Finite Supersoluble Groups." Algebra Colloquium 16, no. 02 (June 2009): 333–40. http://dx.doi.org/10.1142/s1005386709000327.

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Let H and T be subgroups of a finite group G. We say that H is completely c-permutable with T in G if there exists an element x ∈ 〈H,T〉 such that HTx = TxH. In this paper, we use this concept to determine the supersolubility of a group G = AB, where A and B are supersoluble subgroups of G. Some criterions of supersolubility of such groups are obtained and some known results are generalized.
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21

Robinson, Derek J. S. "Book Review: Products of groups." Bulletin of the American Mathematical Society 30, no. 2 (April 1, 1994): 262–69. http://dx.doi.org/10.1090/s0273-0979-1994-00460-4.

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22

May, Coy L., and Jay Zimmerman. "Subdirect products of $M^*$-groups." Rocky Mountain Journal of Mathematics 42, no. 5 (October 2012): 1561–82. http://dx.doi.org/10.1216/rmj-2012-42-5-1561.

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23

Passman, D. S. "Free products in linear groups." Proceedings of the American Mathematical Society 132, no. 1 (May 9, 2003): 37–46. http://dx.doi.org/10.1090/s0002-9939-03-07033-3.

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24

Curzio, Mario, Patrizia Longobardi, Mercede Maj, and Akbar Rhemtulla. "Groups with many rewritable products." Proceedings of the American Mathematical Society 115, no. 4 (April 1, 1992): 931. http://dx.doi.org/10.1090/s0002-9939-1992-1086580-x.

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25

Cossey, John, and Stewart E. Stonehewer. "Products of finite nilpotent groups." Communications in Algebra 27, no. 1 (January 1999): 289–300. http://dx.doi.org/10.1080/00927879908826432.

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26

Elashiry, M. I. "Groups with Many Rewritable Products." Communications in Algebra 41, no. 6 (May 21, 2013): 2132–38. http://dx.doi.org/10.1080/00927872.2012.654416.

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27

Henriksen, M., R. Kopperman, and F. A. Smith. "Ordered products of topological groups." Mathematical Proceedings of the Cambridge Philosophical Society 102, no. 2 (September 1987): 281–95. http://dx.doi.org/10.1017/s030500410006730x.

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The topology most often used on a totally ordered group (G, <) is the interval topology. There are usually many ways to totally order G x G (e.g., the lexicographic order) but the interval topology induced by such a total order is rarely used since the product topology has obvious advantages. Let ℝ(+) denote the real line with its usual order and Q(+) the subgroup of rational numbers. There is an order on Q x Q whose associated interval topology is the product topology, but no such order on ℝ x ℝ can be found. In this paper we characterize those pairs G, H of totally ordered groups such that there is a total order on G x H for which the interval topology is the product topology.
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28

CHISWELL, I. M. "ORDERING GRAPH PRODUCTS OF GROUPS." International Journal of Algebra and Computation 22, no. 04 (June 2012): 1250037. http://dx.doi.org/10.1142/s0218196712500373.

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It is shown that a graph product of right-orderable groups is right orderable, and that a graph product of (two-sided) orderable groups is orderable. The latter result makes use of a new way of ordering free products of groups.
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29

IVANOV, SERGEI V. "ON PERIODIC PRODUCTS OF GROUPS." International Journal of Algebra and Computation 05, no. 01 (February 1995): 7–17. http://dx.doi.org/10.1142/s0218196795000033.

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Adian introduced periodic n-products of groups which are given by imposing of defining relations of the form An=1 on the free product [Formula: see text] of groups Gα, α∈I, without involutions. The defining relations An=1 are constructed by a complicated induction which is quite similar to the inductive construction of free Burnside groups due to Novikov and Adian. This periodic n-product [Formula: see text] of groups Gα, α∈I, has the remarkable property that for every [Formula: see text] either xn=1 or x is conjugate to an element of Gα for some α. The main result of the article is that this property of periodic n-product can be taken as its definition. This gives a new non-inductive characterization of periodic n-products. An analogous characterization of periodic [Formula: see text]-products due to Ol’shanskii is also given.
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30

Kim, P. S., and A. H. Rhemtulla. "Permutable word products in groups." Bulletin of the Australian Mathematical Society 40, no. 2 (October 1989): 243–54. http://dx.doi.org/10.1017/s0004972700004354.

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Let u(x1,…,xn) = x11 … x1m be a word in the alphabet x1, …,xn such that x1i ≠ x1i for all i = 1,…, m − 1. If (H1, …, Hn) is an n-tuple of subgroups of a group G then denote by u(H1, …, Hn) the set {u(h1,…,hn) | hi ∈ Hi}. If σ ∈ Sn then denote by uσ(H1,…,Hn) the set u(Hσ(1),…,Hσ(n)). We study groups G with the property that for each n-tuple (H1,…,Hn) of subgroups of G, there is some σ ∈ Sn σ ≠ 1 such that u(H1,…,Hn) = uσ(H1,…,Hn). If G is a finitely generated soluble group then G has this property for some word u if and only if G is nilpotent-by-finite. In the paper we also look at some specific words u and study the properties of the associated groups.
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31

Chigogidze, A. "Valdivia compact groups are products." Topology and its Applications 155, no. 6 (February 2008): 605–9. http://dx.doi.org/10.1016/j.topol.2007.12.003.

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32

Brandl, Rolf. "CLT groups and wreath products." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 42, no. 2 (April 1987): 183–95. http://dx.doi.org/10.1017/s1446788700028196.

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AbstractIn this paper the question is considered of when the wreath product of a nilpotent group with a CLT group G is a CLT group. It is shown that if the field with Pr elements is a splitting field of a Hall P1–subgroup of G, then P wr G is a CLT group for all p–groups P with |P/P1|≥ pr. Moreover, the class of all groups G having the property that N wr G is a CLT group for every nilpotent group N is shown to be quite large. For exmple, every group of odd order can be embedded as a subgroup of a group belonging to this class.
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33

Dikranjan, D. N., and D. B. Shakhmatov. "Products of minimal Abelian groups." Mathematische Zeitschrift 204, no. 1 (December 1990): 583–603. http://dx.doi.org/10.1007/bf02570894.

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34

Alejandre, Manuel J., A. Ballester-Bolinches, and John Cossey. "Permutable products of supersoluble groups." Journal of Algebra 276, no. 2 (June 2004): 453–61. http://dx.doi.org/10.1016/j.jalgebra.2003.01.002.

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35

Heineken, Hermann. "Products of finite nilpotent groups." Mathematische Annalen 287, no. 1 (March 1990): 643–52. http://dx.doi.org/10.1007/bf01446920.

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36

Almazar, Vittorio D., and John Cossey. "Polycyclic products of nilpotent groups." Archiv der Mathematik 66, no. 1 (January 1996): 1–7. http://dx.doi.org/10.1007/bf01323976.

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37

Brooksbank, Peter A., and James B. Wilson. "Groups acting on tensor products." Journal of Pure and Applied Algebra 218, no. 3 (March 2014): 405–16. http://dx.doi.org/10.1016/j.jpaa.2013.06.011.

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38

Robinson, Derek J. S. "Soluble products of nilpotent groups." Journal of Algebra 98, no. 1 (January 1986): 183–96. http://dx.doi.org/10.1016/0021-8693(86)90021-9.

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39

Zhou, Fang, and Heguo Liu. "Automorphism groups of semidirect products." Archiv der Mathematik 91, no. 3 (August 15, 2008): 193–98. http://dx.doi.org/10.1007/s00013-008-2726-5.

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40

Agore, A. L., A. Chirvăsitu, B. Ion, and G. Militaru. "Bicrossed Products for Finite Groups." Algebras and Representation Theory 12, no. 2-5 (March 3, 2009): 481–88. http://dx.doi.org/10.1007/s10468-009-9145-6.

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41

Ershov, Yu L. "Projective products of profinite groups." Algebra and Logic 30, no. 6 (November 1991): 417–26. http://dx.doi.org/10.1007/bf02018737.

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42

Hofmann, Eric. "Borcherds products on unitary groups." Mathematische Annalen 358, no. 3-4 (September 28, 2013): 799–832. http://dx.doi.org/10.1007/s00208-013-0966-6.

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43

Wang, Shuzhou. "Tensor Products and Crossed Products of Compact Quantum Groups." Proceedings of the London Mathematical Society s3-71, no. 3 (November 1995): 695–720. http://dx.doi.org/10.1112/plms/s3-71.3.695.

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44

Kim, Goan-Su. "OUTER AUTOMORPHISM GROUPS OF CERTAIN POLYGONAL PRODUCTS OF GROUPS." Bulletin of the Korean Mathematical Society 45, no. 1 (February 29, 2008): 45–52. http://dx.doi.org/10.4134/bkms.2008.45.1.045.

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45

Odoni, R. W. K. "Realising wreath products of cyclic groups as Galois groups." Mathematika 35, no. 1 (June 1988): 101–13. http://dx.doi.org/10.1112/s002557930000632x.

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46

Kaheni, Azam, Azam Hokmabadi, and Saeed Kayvanfar. "Nilpotent Products of Cyclic Groups and Classification ofp-Groups." Communications in Algebra 41, no. 1 (January 31, 2013): 154–59. http://dx.doi.org/10.1080/00927872.2011.624148.

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47

du Sautoy, Marcus. "ZETA FUNCTIONS OF GROUPS: EULER PRODUCTS AND SOLUBLE GROUPS." Proceedings of the Edinburgh Mathematical Society 45, no. 1 (February 2002): 149–54. http://dx.doi.org/10.1017/s0013091500000456.

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AbstractThe well-behaved Sylow theory for soluble groups is exploited to prove an Euler product for zeta functions counting certain subgroups in pro-soluble groups. This generalizes a result of Grunewald, Segal and Smith for nilpotent groups.AMS 2000 Mathematics subject classification: Primary 20F16; 11M99
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48

Pyrch, N. M. "Free paratopological groups and free products of paratopological groups." Journal of Mathematical Sciences 174, no. 2 (March 12, 2011): 190–95. http://dx.doi.org/10.1007/s10958-011-0289-7.

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49

Cutolo, Giovanni, Howard Smith, and James Wiegold. "Wreath products of cyclic p-groups as automorphism groups." Journal of Algebra 282, no. 2 (December 2004): 610–25. http://dx.doi.org/10.1016/j.jalgebra.2003.08.023.

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50

Marín, Víctor, and Héctor Pinedo. "Groupoids: Direct products, semidirect products and solvability." Algebra and Discrete Mathematics 33, no. 2 (2022): 92–107. http://dx.doi.org/10.12958/adm1772.

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We present some constructions of groupoids such as: direct product, semidirect product and give necessary and sufficient conditions for a groupoid to be embedded into a direct product of groupoids. Also, we establish necessary and sufficient conditions to determine when a semidirect product is direct. Finally the notion of solvable groupoid is introduced and studied, in particular it is shown that a finite groupoid G is solvable if and only if its isotropy groups are.
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