Miao, Long Qian, Guohua
Published in
Siberian Mathematical Journal

A subgroup H is called ℳ-supplemented in a finite group G, if there exists a subgroup B of G such that G = HB and H1B is a proper subgroup of G for every maximal subgroup H1 of H. We investigate the influence of ℳ-supplementation of Sylow subgroups and obtain a condition for solvability and p-supersolvability of finite groups.

Stetkær, Henrik
Published in
Aequationes mathematicae

We study properties of solutions f of d’Alembert’s functional equations on a topological group G. For nilpotent groups and for connected, solvable Lie groups G, we prove that f has the form \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \us...

Bludov, V. V. Kopytov, V. M. Rhemtulla, A. H.
Published in
Algebra and Logic

Orderable solvable groups in which every relatively convex subgroup is normal are studied. If such a class is subgroup closed than it is precisely the class of solvable orderable groups which are locally of finite (Mal’tsev) rank. A criterion for an orderable metabelian group to have every relatively convex subgroup normal is given. Examples of an ...

Monakhov, V. S. Borodich, T. V.
Published in
Mathematical Notes

The solvability of any finite group with Hall supplements to normalizers of the Sylow subgroups is established.

Dashkova, O. Yu.
Published in
Siberian Mathematical Journal

Under study are the solvable nonabelian linear groups of infinite central dimension and sectional p-rank, p ≥ 0, in which all proper nonabelian subgroups of infinite sectional p-rank have finite central dimension. We describe the structure of the groups of this class.

Knyagina, V. N. Monakhov, V. S.
Published in
Algebra and Logic

A non-nilpotent finite group whose proper subgroups are all nilpotent is called a Schmidt group. A subgroup A is said to be seminormal in a group G if there exists a subgroup B such that G = AB and AB1 is a proper subgroup of G, for every proper subgroup B1 of B. Groups that contain seminormal Schmidt subgroups of even order are considered. In part...

Guo, W. Shum, K. P. Skiba, A. N.
Published in
Siberian Mathematical Journal

Considering two subgroups A and B of a group G and ⊘ ≠ X ⊆ G, we say that A is X-permutable with B if ABx = BxA for some element x ∈ X. We use this concept to give new characterizations of the classes of solvable, supersolvable, and nilpotent finite groups.

Monakhov, V. S. Tyutyanov, V. N.
Published in
Siberian Mathematical Journal

We establish the solvability of each finite group whose every proper nonmaximal subgroup lies in some subgroup of prime index.

Monakhov, V. S.
Published in
Mathematical Notes

Tests for π-solvability of a finite group with seminormal Hall π-subgroup are established and the nilpotency of the third commutator subgroup of any group with seminormal noncyclic Sylow subgroups is proved.

Gupta, Ch. K. Timoshenko, E. I.
Published in
Siberian Mathematical Journal

We study the first-order definable, Diophantine, and algebraic subsets in the set of all ordered sets generating a group or generating a group as a normal subgroup for some relatively free solvable groups.