On some elementary properties of soluble groups of derived length 2.
On some infinite dimensional linear groups
Let F be a field, A be a vector space over F, and GL(F,A) the group of all automorphisms of the vector space A. A subspace B of A is called nearly G-invariant, if dimF(BFG/B) is finite. A subspace B is called almost G-invariant, if dimF(B/CoreG(B)) is finite. In the present article we begin the study of subgroups G of GL(F,A) such that every subspace of A is either nearly G-invariant or almost G-invariant. More precisely, we consider the case when G is a periodic p′-group where p = charF.
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 some soluble groups in which -subgroups form a lattice
The article is dedicated to groups in which the set of abnormal and normal subgroups (-subgroups) forms a lattice. A complete description of these groups under the additional restriction that every counternormal subgroup is abnormal is obtained.
On tame automorphisms of some metabelian groups.
On the Cantor-Bendixson rank of metabelian groups
We study the Cantor-Bendixson rank of metabelian and virtually metabelian groups in the space of marked groups, and in particular, we exhibit a sequence of 2-generated, finitely presented, virtually metabelian groups of Cantor-Bendixson rank .
On the derived length of parasoluble groups
In this paper groups are considered inducing groups of power automorphisms on each factor of their derived series. In particular, it is proved that soluble groups with such property have derived length at most 3, and that this bound is best possible.
On the group of reduced identities of relatively free solvable groups.
On transitivity of pronormality
This article is dedicated to soluble groups, in which pronormality is a transitive relation. Complete description of such groups is obtained.
On universal theories of metabelian groups and the Shmel'kin embedding.