Results 131 to 140 of about 19,998 (174)

Locally finite groups with a nilpotent or locally nilpotent maximal subgroup

Journal of Group Theory, 1999
The authors, especially the first author, continue their study of locally nilpotent maximal subgroups of locally finite groups. Here, they prove the following: Let \(G\) be a locally finite group and \(H\) a locally nilpotent maximal subgroup of \(G\) such that \(\bigcap_{g\in G}H^g=\langle 1\rangle\). Theorem A. Suppose \(H\) is an FC-group.
Bruno, Brunella, Napolitani, Franco
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Local rings whose multiplicative group is nilpotent

Archiv der Mathematik, 2003
It is shown that the \(n\)-th term of the upper central series of the multiplicative group of a local ring \(R\) coincides with the multiplicative group of the \(n\)-th term of the upper central series of the associated Lie ring of \(R\). In particular, the multiplicative group of \(R\) is nilpotent if and only if the associated Lie ring of \(R\) is ...
Catino, F., Miccoli, M. M.
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Locally Nilpotent Finitary Skew Linear Groups

Journal of the London Mathematical Society, 1994
A number of division rings arising from free groups, from certain soluble groups or from certain Lie algebras are locally residually finite- dimensional in a particular sense. In two earlier papers [J. Pure Appl. Algebra 60, No. 3, 289-312 (1989; Zbl 0688.20030), Fundam. Math.
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A (locally nilpotent)-by-nilpotent variety of groups

Mathematical Proceedings of the Cambridge Philosophical Society, 2002
Given positive integers k and n, let [Xfr ] be the class of all groups G such that γk(G) is locally nilpotent and [x1, x2, …, xk]n = 1 for any x1, x2, …, xk ∈ G. It is shown that [Xfr ] is a variety.
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Factorization of Periodic Locally Solvable Groups by Locally Nilpotent and Nilpotent Subgroups

Ukrainian Mathematical Journal, 2001
The paper continues a series of four papers of the author [see Ukr. Mat. Zh. 53, No. 4, 531-541 (2001; Zbl 0992.20016), ibid. 52, No. 6, 809-819 (2000; Zbl 0956.20012), ibid. 52, No. 7, 965-970 (2000; Zbl 0956.20038), Vopr. Algebry 11, 90-115 (1997; Zbl 0912.20023)] which deal with products of two groups.
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Locally Finite Products of Totally Permutable Nilpotent Groups

Algebra Colloquium, 2009
A group G=AB is said to be totally factorized by its subgroups A and B if XY=YX for all subgroups X of A and Y of B. It is known that any finite group totally factorized by supersoluble subgroups is supersoluble, and that a finite group totally factorized by nilpotent subgroups is abelian-by-nilpotent.
DE FALCO, MARIA, DE GIOVANNI, FRANCESCO, MUSELLA, CARMELA   +2 more
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Localization of nilpotent R-powered groups

Journal of Group Theory, 2012
AbstractIn this paper, we generalize portions of the theory of localization to the category of ...
Stephen Majewicz, Marcos Zyman
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On Minimal Non-(residually Nilpotent) Locally Graded Groups

Mediterranean Journal of Mathematics, 2021
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Virtually Nilpotent Groups with (almost) All Localizations Trivial

Mathematische Nachrichten, 2000
A group \(G\) is generically trivial if and only if, for all prime numbers \(p\), the localization of \(G\) with respect to \(p\) is trivial (or equivalently, \(G\) belongs to the Mislin genus of the trivial group). The authors prove that a virtually nilpotent group \(G\) (which is an extension of a nilpotent group by a finite group) is generically ...
Descheemaeker, An, Malfait, Wim
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Group Algebras with Locally Nilpotent Unit Groups

Communications in Algebra, 2015
Let F be a field of characteristic p ≥ 0 and G any group. The local nilpotency of the group of units of the group algebra FG is investigated. We show that if 𝒰(FG) is locally nilpotent, then the set of p-elements of G form a subgroup P and the torsion elements of G/P form an abelian group. If, in addition, the set of nilpotent elements of FG is
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