Results 11 to 20 of about 301 (136)
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
doaj +1 more source
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
doaj +1 more source
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
doaj +1 more source
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
doaj +1 more source
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
doaj +1 more source
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
doaj +1 more source
From Groups to Leibniz Algebras: Common Approaches, Parallel Results [PDF]
Advances in Group Theory and Applications, 2018 In this article, we study (locally) nilpotent and hyper-central Leibniz algebras. We obtained results similar to those in group theory. For instance, we proved a result analogous to the Hirsch-Plotkin Theorem for locally nilpotent groups.
L.A. Kurdachenko +2 more
doaj +1 more source
Endomorphism kernel property for finite groups [PDF]
Mathematica Bohemica, 2022 A group $G$ has the endomorphism kernel property (EKP) if every congruence relation $\theta$ on $G$ is the kernel of an endomorphism on $G$. In this note we show that all finite abelian groups have EKP and we show infinite series of finite non-abelian ...
Heghine Ghumashyan, Jaroslav Guričan
doaj +1 more source
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
doaj +1 more source
The Electronic Journal of Combinatorics, 2006 Let $N$ be a nilpotent group normal in a group $G$. Suppose that $G$ acts transitively upon the points of a finite non-Desarguesian projective plane ${\cal P}$. We prove that, if ${\cal P}$ has square order, then $N$ must act semi-regularly on ${\cal P}$.
openaire +4 more sources