On multipliers of Heineken-Mohamed type groups
On non-periodic groups whose finitely generated subgroups are either permutable or pronormal
The current article considers some infinite groups whose finitely generated subgroups are either permutable or pronormal. A group is called a generalized radical, if has an ascending series whose factors are locally nilpotent or locally finite. The class of locally generalized radical groups is quite wide. For instance, it includes all locally finite, locally soluble, and almost locally soluble groups. The main result of this paper is the followingTheorem. Let be a locally generalized radical...
On products of soluble groups of finite rank.
On semiabelian groups.
On some properties of pronormal subgroups
New results on tight connections among pronormal, abnormal and contranormal subgroups of a group have been established. In particular, new characteristics of pronormal and abnormal subgroups have been obtained.
On subnormal series with factors of finite rank : the join problem
On the Boffa alternative
Let G* denote a nonprincipal ultrapower of a group G. In 1986 M.~Boffa posed a question equivalent to the following one: if G does not satisfy a positive law, does G* contain a free nonabelian subsemigroup? We give the affirmative answer to this question in the large class of groups containing all residually finite and all soluble groups, in fact, all groups considered in traditional textbooks on group theory.
On the exponent of the product of two groups
On the Fixed-Point Set and Commutator Subgroup of an Automorphism of a Group of Finite Rank
On the power-commutative kernel of locally nilpotent groups.
On the relations between the central factor-module and the derived submodule in modules over group rings
A modular analogue of the well-known group theoretical result about finiteness of the derived subgroup in a group with a finite factor by its center has been obtained.
On the structure of the normal subgroups of a group : supersolubility
Periodic-by-nilpotent linear groups
Polycyclic groups, Lie algebras and algebraic groups.
Pronormality, contranormality and generalized nilpotency in infinite groups.
This article is dedicated to some criteria of generalized nilpotency involving pronormality and abnormality. Also new results on groups, in which abnormality is a transitive relation, have been obtained.
Remarks on the Mal'cev completion of torsion-free locally nilpotent groups
Soluble Products of Polycyclic Groups.
Some properties of generalized wreath products
Some questions on quasinilpotent groups and related classes.
In this paper we will prove that if G is a finite group, X a subnormal subgroup of X F*(G) such that X F*(G) is quasinilpotent and Y is a quasinilpotent subgroup of NG(X), then Y F*(NG(X)) is quasinilpotent if and only if Y F*(G) is quasinilpotent. Also we will obtain that F*(G) controls its own fusion in G if and only if G = F*(G).
Some remarks on almost finitely generated nilpotent groups.
We identify two generalizations of the notion of a finitely generated nilpotent. Thus a nilpotent group G is fgp if Gp is fg as p-local group for each p; and G is fg-like if there exists a fg nilpotent group H such that Gp ≅ Hp for all p. The we have proper set-inclusions:{fg} ⊂ {fg-like} ⊂ {fgp}.We examine the extent to which fg-like nilpotent groups satisfy the axioms for a Serre class. We obtain a complete answer only in the case that [G, G] is finite. (The collection of fgp nilpotent groups...