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Journal articles on the topic 'Finite soluble groups'

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Published: 4 June 2021

Last updated: 28 January 2023

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1

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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2

Adarchenko, N. M. "A new characterization of finite σ-soluble PσT-groups." Algebra and Discrete Mathematics 29, no. 1 (2020): 33–41. http://dx.doi.org/10.12958/adm1530.

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3

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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4

Huang, J., B. Hu, and A. N. Skiba. "Finite Generalized Soluble Groups." Algebra and Logic 58, no. 2 (May 2019): 173–85. http://dx.doi.org/10.1007/s10469-019-09535-1.

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5

Kovács, L. G., and Hyo-Seob Sim. "Generating finite soluble groups." Indagationes Mathematicae 2, no. 2 (June 1991): 229–32. http://dx.doi.org/10.1016/0019-3577(91)90009-v.

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6

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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7

Praeger, Cheryl E. "Book Review: Finite soluble groups." Bulletin of the American Mathematical Society 29, no. 1 (July 1, 1993): 104–7. http://dx.doi.org/10.1090/s0273-0979-1993-00388-4.

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8

Li, Cai Heng. "Finite CI-Groups are Soluble." Bulletin of the London Mathematical Society 31, no. 4 (July 1999): 419–23. http://dx.doi.org/10.1112/s0024609399005901.

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9

Ballester-Bolinches, A., and M. D. Pérez-Ramos. "Permutability in finite soluble groups." Mathematical Proceedings of the Cambridge Philosophical Society 115, no. 3 (May 1994): 393–96. http://dx.doi.org/10.1017/s0305004100072182.

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Let G be a finite soluble group and let Σ be a Hall system of G. A subgroup U of G is said to be Σ-permutable if U permutes with every member of Σ. In [1; I, 4·29] it is proved that if U and V are Σ-permutable subgroups of G then so also are U ∩ V and 〈U, V〉.

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10

Linnell, P. A. "Cohomology of finite soluble groups." Journal of Algebra 107, no. 1 (April 1987): 53–62. http://dx.doi.org/10.1016/0021-8693(87)90072-x.

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11

Dixon, Martyn R., Martin J. Evans, and Howard Smith. "Locally (Soluble-by-Finite) Groups of Finite Rank." Journal of Algebra 182, no. 3 (June 1996): 756–69. http://dx.doi.org/10.1006/jabr.1996.0200.

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12

Nikolov, Nikolay, and Dan Segal. "A characterization of finite soluble groups." Bulletin of the London Mathematical Society 39, no. 2 (February 13, 2007): 209–13. http://dx.doi.org/10.1112/blms/bdl028.

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13

Shumyatsky, Pavel. "Fixed Points in Finite Soluble Groups#." Communications in Algebra 33, no. 10 (September 2005): 3405–8. http://dx.doi.org/10.1080/agb-200061471.

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14

Kazarin, Lev S., and Evgenii I. Chankov. "Finite simply reducible groups are soluble." Sbornik: Mathematics 201, no. 5 (June 29, 2010): 655–68. http://dx.doi.org/10.1070/sm2010v201n05abeh004087.

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15

Glasby, S. P. "Constructing normalisers in finite soluble groups." Journal of Symbolic Computation 5, no. 3 (June 1988): 285–94. http://dx.doi.org/10.1016/s0747-7171(88)80030-0.

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16

Glasby, S. P. "Intersecting subgroups of finite soluble groups." Journal of Symbolic Computation 5, no. 3 (June 1988): 295–301. http://dx.doi.org/10.1016/s0747-7171(88)80031-2.

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17

Cossey, John. "Finite soluble groups have large centralisers." Bulletin of the Australian Mathematical Society 35, no. 2 (April 1987): 291–98. http://dx.doi.org/10.1017/s0004972700013241.

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We say that a finite group G has a large centraliser if G contains a non-central element x with |CG (x)| > |G|½. We prove that every finite soluble group has a large centraliser, confirming a conjecture of Bertram and Herzog.

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18

Smith, Michael J. "Computing automorphisms of finite soluble groups." Bulletin of the Australian Mathematical Society 53, no. 1 (February 1996): 169–71. http://dx.doi.org/10.1017/s0004972700016841.

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19

Wetherell, C. J. T. "Subnormal structure of finite soluble groups." Bulletin of the Australian Mathematical Society 66, no. 1 (August 2002): 171. http://dx.doi.org/10.1017/s0004972700020797.

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20

Casolo, Carlo. "Subnormality in factorizable finite soluble groups." Archiv der Mathematik 57, no. 1 (July 1991): 12–13. http://dx.doi.org/10.1007/bf01200032.

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21

Heineken, Hermann. "Nilpotent subgroups of finite soluble groups." Archiv der Mathematik 56, no. 5 (May 1991): 417–23. http://dx.doi.org/10.1007/bf01200083.

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22

Bashun, S. Yu, and E. M. Palchik. "On Soluble Radicals of Finite Groups." Ukrainian Mathematical Journal 72, no. 3 (August 2020): 370–85. http://dx.doi.org/10.1007/s11253-020-01788-9.

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23

Li, Jinbao, and Yong Yang. "A characterization of finite soluble groups." Communications in Algebra 49, no. 1 (August 10, 2020): 310–16. http://dx.doi.org/10.1080/00927872.2020.1798977.

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24

Guo, Wenbin, and N. T. Vorob'ev. "On Injectors Of Finite Soluble Groups." Communications in Algebra 36, no. 9 (September 17, 2008): 3200–3208. http://dx.doi.org/10.1080/00927870802103560.

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25

Amberg, Bernhard, and Lev S. Kazarin. "On finite products of soluble groups." Israel Journal of Mathematics 106, no. 1 (December 1998): 93–108. http://dx.doi.org/10.1007/bf02773462.

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26

Ballester-Bolinches, Adolfo, John Cossey, and Liangcai Zhang. "Generalised norms in finite soluble groups." Journal of Algebra 402 (March 2014): 392–405. http://dx.doi.org/10.1016/j.jalgebra.2013.12.012.

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27

Casolo, Carlo, and Enrico Jabara. "Finite soluble groups with metabelian centralizers." Journal of Algebra 422 (January 2015): 318–33. http://dx.doi.org/10.1016/j.jalgebra.2014.09.032.

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28

Casolo, Carlo. "Soluble Groups with Finite Wielandt length." Glasgow Mathematical Journal 31, no. 3 (September 1989): 329–34. http://dx.doi.org/10.1017/s0017089500007898.

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The Wielandt subgroup ω(G) of a group G is defined to be the intersection of all normalizers of subnormal subgroups of G; the terms of the Wielandt series of G are defined, inductively, by putting ω0(G) = 1 and (ωn+1(G)/ωn(G) = ω(G/ωn(G)). If, for some integer n, ωn(G) = G, then G is said to have finite Wielandt length; the Wielandt length of G being the minimal n such that ωn(G) = G.

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29

Azarov, D. N. "Approximability of finite rank soluble groups by certain classes of finite groups." Russian Mathematics 58, no. 8 (July 18, 2014): 15–23. http://dx.doi.org/10.3103/s1066369x14080027.

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30

Groves, J. R. J., and G. C. Smith. "Soluble groups with a finite rewriting system." Proceedings of the Edinburgh Mathematical Society 36, no. 2 (June 1993): 283–88. http://dx.doi.org/10.1017/s0013091500018381.

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We describe a class of soluble groups with a finite complete rewriting system which includes all the soluble groups known to have such a system. It is an open question, related to deep questions in the theory of groups, whether it includes all soluble groups with such a system.

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31

Ballester-Bolinches, Adolfo, John Cossey, and Yangming Li. "On a class of finite soluble groups." Journal of Group Theory 21, no. 5 (September 1, 2018): 839–46. http://dx.doi.org/10.1515/jgth-2018-0015.

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Abstract The aim of this paper is to study the class of finite groups in which every subgroup is self-normalising in its subnormal closure. It is proved that this class is a subgroup-closed formation of finite soluble groups which is not closed under taking Frattini extensions and whose members can be characterised by means of their Carter subgroups. This leads to new characterisations of finite soluble T-, PT- and PST-groups. Finite groups whose p-subgroups, p a prime, are self-normalising in their subnormal closure are also characterised.

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32

Martinez, Consuelo. "Power Subgroups of Pro-(Finite Soluble) Groups." Bulletin of the London Mathematical Society 28, no. 5 (September 1996): 481–87. http://dx.doi.org/10.1112/blms/28.5.481.

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33

Monakhov, V. S., and A. A. Trofimuk. "On finite soluble groups of fixed rank." Siberian Mathematical Journal 52, no. 5 (September 2011): 892–903. http://dx.doi.org/10.1134/s0037446611050144.

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34

Bryce, R. A. "Subgroups like Wielandt's in finite soluble groups." Mathematical Proceedings of the Cambridge Philosophical Society 107, no. 2 (March 1990): 239–59. http://dx.doi.org/10.1017/s0305004100068511.

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In 1935 Baer[1] introduced the concept of kern of a group as the subgroup of elements normalizing every subgroup of the group. It is of interest from three points of view: that of its structure, the nature of its embedding in the group, and the influence of its internal structure on that of the whole group. The kern is a Dedekind group because all its subgroups are normal. Its structure is therefore known exactly (Dedekind [7]): if not abelian it is a direct product of a copy of the quaternion group of order 8 and an abelian periodic group with no elements of order 4. As for the embedding of the kern, Schenkman[13] shows that it is always in the second centre of the group: see also Cooper [5], theorem 6·5·1. As an example of the influence of the structure of the kern on its parent group we cite Baer's result from [2], p. 246: among 2-groups, only Hamiltonian groups (i.e. non-abelian Dedekind groups) have nonabelian kern.

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35

Ballester-Bolinches, Adolfo, Enric Cosme-Llópez, and Sergey Fedorovich Kamornikov. "On subgroup functors of finite soluble groups." Science China Mathematics 60, no. 3 (October 17, 2016): 439–48. http://dx.doi.org/10.1007/s11425-015-0330-9.

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36

Crestani, Eleonora, and Andrea Lucchini. "The generating graph of finite soluble groups." Israel Journal of Mathematics 198, no. 1 (January 22, 2013): 63–74. http://dx.doi.org/10.1007/s11856-012-0190-1.

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37

Fedri, V., and L. Serena. "Finite soluble groups with supersoluble Sylow normalizers." Archiv der Mathematik 50, no. 1 (January 1988): 11–18. http://dx.doi.org/10.1007/bf01313488.

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38

Alejandre, Manuel J., A. Ballester-Bolinches, and M. C. Pedraza-Aguilera. "Finite Soluble Groups with Permutable Subnormal Subgroups." Journal of Algebra 240, no. 2 (June 2001): 705–22. http://dx.doi.org/10.1006/jabr.2001.8732.

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39

Franciosi, Silvana, and Francesco de Giovanni. "On trifactorized soluble groups of finite rank." Geometriae Dedicata 38, no. 3 (June 1991): 331–41. http://dx.doi.org/10.1007/bf00181195.

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40

Robinson, Derek J. S. "On the cohomology of finite soluble groups." Archiv der Mathematik 105, no. 2 (July 12, 2015): 101–8. http://dx.doi.org/10.1007/s00013-015-0790-1.

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41

Ballester-Bolinches, A. "Permutably embedded subgroups of finite soluble groups." Archiv der Mathematik 65, no. 1 (July 1995): 1–7. http://dx.doi.org/10.1007/bf01196571.

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42

Iranzo, M. J., Julio P. Lafuente, and F. Pérez-Monasor. "On sylowizers in finite p-soluble groups." Ricerche di Matematica 56, no. 2 (November 16, 2007): 189–94. http://dx.doi.org/10.1007/s11587-007-0012-7.

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43

Badis, Abdelhafid, and Nadir Trabelsi. "Soluble minimal non-(finite-by-Baer)-groups." Ricerche di Matematica 59, no. 1 (December 4, 2009): 129–35. http://dx.doi.org/10.1007/s11587-009-0070-0.

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44

Baumeister, Barbara. "A characterization of the finite soluble groups." Archiv der Mathematik 72, no. 3 (March 1999): 167–76. http://dx.doi.org/10.1007/s000130050318.

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45

Lucchini, Andrea. "Finite soluble groups satisfying the swap conjecture." Journal of Algebraic Combinatorics 42, no. 4 (June 9, 2015): 907–15. http://dx.doi.org/10.1007/s10801-015-0610-5.

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46

Leinen, Felix. "An Amalgamation Theorem For Soluble Groups." Canadian Mathematical Bulletin 30, no. 1 (March 1, 1987): 9–18. http://dx.doi.org/10.4153/cmb-1987-002-7.

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AbstractA theorem of G. Higman about the embeddability of amalgams within the class of all finite ρ-groups is generalized to classes of soluble groups. We also give best possible bounds for the solubility lengths of the constructed completions. And, as an application, the super-soluble amalgamation bases in the class of all finite soluble π-groups are determined.

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47

Wehrfritz, Bertram A. F. "Automorphisms of Finite Order of Soluble Groups of Finite Rank." Studia Scientiarum Mathematicarum Hungarica 58, no. 1 (April 14, 2021): 19–31. http://dx.doi.org/10.1556/012.2021.58.1.1486.

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We study the effect on sections of a soluble-by-finite group G of finite rank of an almost fixed-point-free automorphism φ of G of finite order. We also elucidate the structure of G if φ has order 4 and if G is also (torsion-free)-by-finite. The latter extends recent work of Xu, Zhou and Liu.

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48

KHUKHRO, E. I. "ON SOLUBILITY OF GROUPS WITH BOUNDED CENTRALIZER CHAINS." Glasgow Mathematical Journal 51, no. 1 (January 2009): 49–54. http://dx.doi.org/10.1017/s0017089508004527.

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AbstractThe c-dimension of a group is the maximum length of a chain of nested centralizers. It is proved that a periodic locally soluble group of finite c-dimension k is soluble of derived length bounded in terms of k, and the rank of its quotient by the Hirsch–Plotkin radical is bounded in terms of k. Corollary: a pseudo-(finite soluble) group of finite c-dimension k is soluble of derived length bounded in terms of k.

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49

Heineken, Hermann. "Hypernormalizing groups." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 47, no. 2 (October 1989): 211–25. http://dx.doi.org/10.1017/s1446788700031645.

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AbstractAll subnormal subgroups of hypernormalizing groups have by definition subnormal normalizers. It is shown that finite soluble HN-groups belong to the class of groups of Fitting length three. Finite HN-groups are considered including those with subnormal quotient isomorphic to SL(2,5).

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50

Wilson, John S. "Soluble Groups Which are Products of Groups of Finite Rank." Journal of the London Mathematical Society s2-40, no. 3 (December 1989): 405–19. http://dx.doi.org/10.1112/jlms/s2-40.3.405.

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