Results 41 to 50 of about 5,393,663 (208)
Torsion locally nilpotent groups with non-Dedekind norm of Abelian non-cyclic subgroups
Karpatsʹkì Matematičnì Publìkacìï, 2022 The authors study relations between the properties of torsion locally nilpotent groups and their norms of Abelian non-cyclic subgroups. The impact of the norm of Abelian non-cyclic subgroups on the properties of the group under the condition of norm non ...
T.D. Lukashova, M.G. Drushlyak
doaj +1 more source
Journal of Algebra, 2006 Let \(G\) be a finite group and order the set of sizes of conjugacy classes of \(G\) decreasingly to obtain what is called the conjugate type vector of \(G\). The authors show by examples that if \(H\) is nilpotent and if \(G\) and \(H\) have the same conjugate type vector, then \(G\) is not necessarily nilpotent.
Camina, A.R., Camina, R.D.
openaire +2 more sources
On invariant ideals in group rings of torsion-free minimax nilpotent groups
Researches in Mathematics, 2023 Let $k$ be a field and let $N$ be a nilpotent minimax torsion-free group acted by a solvable group of operators $G$ of finite rank. In the presented paper we study properties of some types of $G$-invariant ideals of the group ring $kN$.
A.V. Tushev
doaj +1 more source
On Torsion-by-Nilpotent Groups
Journal of Algebra, 2001 Here are the main results of the article under review: Theorem 1.1. Let \(\wp\) be a class of groups, which is closed under taking subgroups and quotients. Suppose that all metabelian groups of \(\wp\) are torsion-by-nilpotent. Then all soluble groups of \(\wp\) are torsion-by-nilpotent. Theorem 1.2. Let \(H\) be a normal subgroup of a group \(G\). If \
Endimioni, Gérard, Traustason, Gunnar
openaire +1 more source
Applications of Lie methods to computations with polycyclic groups [PDF]
, 2008 In this thesis we demonstrate the algorithmic usefulness of the so-called Mal'cev correspondence for computations with infinite polycyclic groups.
Assmann, Björn
core +2 more sources
Glasgow Mathematical Journal, 2019 AbstarctLetγn= [x1,…,xn] be thenth lower central word. Denote byXnthe set ofγn-values in a groupGand suppose that there is a numbermsuch that$|{g^{{X_n}}}| \le m$for eachg∈G. We prove thatγn+1(G)has finite (m, n) -bounded order. This generalizes the much-celebrated theorem of B. H. Neumann that says that the commutator subgroup of a BFC-group is finite.
ELOISA DETOMI +3 more
openaire +5 more sources
Ricci-flat and Einstein pseudoriemannian nilmanifolds
Complex Manifolds, 2019 This is partly an expository paper, where the authors’ work on pseudoriemannian Einstein metrics on nilpotent Lie groups is reviewed. A new criterion is given for the existence of a diagonal Einstein metric on a nice nilpotent Lie group.
Conti Diego, Rossi Federico A.
doaj +1 more source
On the structure of groups admitting faithful modules with certain conditions of primitivity
Researches in Mathematics, 2023 In the paper we study structure of soluble-by-finite groups of finite torsion-free rank which admit faithful modules with conditions of primitivity. In particular, we prove that under some additional conditions if an infinite finitely generated linear ...
A.V. Tushev
doaj +1 more source
Locally finite p-groups with all subgroups either subnormal or nilpotent-by-Chernikov [PDF]
International Journal of Group Theory, 2012 We pursue further our investigation, begun in [H.~Smith, Groups with all subgroups subnormal or nilpotent-by-{C}hernikov, emph{Rend. Sem. Mat. Univ. Padova} 126 (2011), 245--253] and continued in [G.~Cutolo and H.~Smith, Locally finite groups with all ...
H. Smith, G. Cutolo
doaj
On Finite Nilpotent Groups [PDF]
Canadian Journal of Mathematics, 1960 It is well known that if (n, ϕ(n)) = 1, where ϕ(n) denotes the Euler ϕ function, then the only group of order n is the cyclic group. This is a special case of a more general result due to Dickson (2, p. 201); namely, ifwhere the pi are distinct primes and each αi > 0, the necessary and sufficient conditions that the only groups of order n are ...
openaire +1 more source