On a class of groups with strongly embedded subgroup.
On a generalization of the Baer-Suzuki theorem.
On absolutely simple locally finite groups
On certain characterizations of barely transitive groups
On cohomological periodicity for infinite groups.
On homomorphic images of locally graded groups
On Locallay Indicable Groups.
On locally finite minimal non-solvable groups
In the present work we consider infinite locally finite minimal non-solvable groups, and give certain characterizations. We also define generalizations of the centralizer to establish a result relevant to infinite locally finite minimal non-solvable groups.
On locally graded barely transitive groups
We show that a barely transitive group is totally imprimitive if and only if it is locally graded. Moreover, we obtain the description of a barely transitive group G for the case G has a cyclic subgroup 〈x〉 which intersects non-trivially with all subgroups and for the case a point stabilizer H of G has a subgroup H 1 of finite index in H satisfying the identity χ(H 1) = 1, where χ is a multi-linear commutator of weight w.
On locally graded non-periodic barely transitive groups
On minimal conditions related to Miller-Moreno 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 -groups with generally finite element.
On pairs of 2-complexes and systems of equations over groups.
On periodic groups with small orders of elements.
On solvable groups of exponent 4.
On some groups with almost regular element of prime order.
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 Burnside problem for groups of even exponent.
On the existence of -local subgroups in a group.