Results 21 to 30 of about 9,042,434 (209)
Torsion Locally Nilpotent Groups with the non-Dedekind Norm of Decomposable Subgroups [PDF]
Advances in Group Theory and Applications, 2023 We study torsion locally nilpotent groups with the non-Dedekind norm of decomposable subgroups. It is found out that such groups are locally finite p-groups. Their structure is described.
Tetiana Lukashova, Marina Drushlyak
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Nilpotent groups are round [PDF]
Israel Journal of Mathematics, 2008 We define a notion of roundness for finite groups. Roughly speaking, a group is round if one can order its elements in a cycle in such a way that some natural summation operators map this cycle into new cycles containing all the elements of the group. Our main result is that this combinatorial property is equivalent to nilpotence.
Berend, Daniel, Boshernitzan, Michael D.
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Omegas of agemos in powerful groups [PDF]
International Journal of Group Theory, 2020 In this note we show that for any powerful $p$-group $G$, the subgroup $\Omega_{i}(G^{p^{j}})$ is powerfully nilpotent for all $i,j\geq1$ when $p$ is an odd prime, and $i\geq1$, $j\geq2$ when $p=2$.
James Williams
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On Some Residual Properties of the Verbal Embeddings of Groups [PDF]
Advances in Group Theory and Applications, 2016 We consider verbal embedding constructions preserving some residual properties for groups. An arbitrary residually finite countable group $H$ has a $V$-verbal embedding into a residually finite $2$-generator group $G$ for any non-trivial word set $V$. If
Vahagn H. Mikaelian
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Enumerating finite class-2-nilpotent groups on 2 generators [PDF]
, 2009 We compute the numbers g(n,2,2) of nilpotent groups of order n, of class atmost 2 generated by at most 2 generators, by giving an explicit formula for theDirichlet generating function \sum_{n=1}^\infty g(n,2,2)n^{-s}
Voll, Christopher, Christopher Voll
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Locally Maximal Subgroups and the Normalizer Condition in p-Groups [PDF]
Advances in Group Theory and Applications, 2023 This work is a continuation of the investigation of a locally nilpotent p-group satisfying the normalizer condition by imposing certain conditions on locally maximal subgroups, where p ≠ 2.
A.O. Asar
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Strongly Ad-Nilpotent Elements of the Lie Algebra of Upper Triangular Matrices
Journal of Mathematics, 2022 In this paper, the strongly ad-nilpotent elements of the Lie algebra tn,ℂ of upper triangular complex matrices are studied. We prove that all the nilpotent matrices in tn,ℂ are strongly ad-nilpotent if and only if n≤6. Additionally, we prove that all the
Zhiguang Hu
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On some commutative invariants of modules over minimax nilpotent groups
Доповiдi Нацiональної академiї наук України, 2022 In the paper we introduce a finite system of invariants for modules over minimax nilpotent groups which consists of classes of equivalent prime ideals of the group algebra of an Abelian minimax group. In particuly, introduced system of invariants allows
A.V. Tushev
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Engel Conditions for Soluble and Pronilpotent Groups [PDF]
Advances in Group Theory and Applications, 2022 Let G be a finitely generated pronilpotent group in which for any elements x, y ∈ G there are positive integers n = n(x, y) and q = q(x, y) such that [x, n y^q] = 1. We show that G is virtually nilpotent.
Pavel Shumyatsky, Wállef da Silva
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Groups whose Proper Subgroups of Infinite Rank are Minimax-by-Nilpotent or Nilpotent-by-Minimax [PDF]
Advances in Group Theory and Applications, 2020 Let M denote the class of of soluble-by-finite minimax groups, and N the class of nilpotent groups. The main result states that if G is a group of infinite rank whose proper subgroups of infinite rank are MN-groups, then G is either in MN or it is a ...
Amel Zitouni
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