Chirik, I. K.
Published in
Mathematical Notes

The solvability of any finite group of the form G = AB is established under the assumption that the subgroups A and B are solvable and KP2-subnormal in the group G.

Krasnikov, A. F.
Published in
Lobachevskii Journal of Mathematics

Let F be a free product of groups Ai (i ∈ I) and a free group G with basis {gjj ∈ J} and its normal subgroup N has trivial intersection with each factor Ai. In this paper we describe an elements v of the group F, such that Dl(v) ≡ 0 mod N, where l belongs to a subset of I ∪ J and Dk: Z(F) → Z(F) (k ∈ I ∪ J) are the Fox derivations of the group ring...

Vdovin, E. P.
Published in
Algebra and Logic

Let a group G contain a Carter subgroup of odd order. It is shown that every composition factor of G either is Abelian or is isomorphic to L2(32n + 1), n ≥ 1. Moreover, if 3 does not divide the order of a Carter subgroup, then G solvable.

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

Given a subgroup A of a group G and some group-theoretic property θ of subgroups, say that A enjoys the gradewise property θ in G whenever G has a normal series \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{...

Vedernikov, V. A.
Published in
Proceedings of the Steklov Institute of Mathematics

We describe finite simple nonabelian groups in which every maximal subgroup is solvable or a Hall subgroup. We also describe nonabelian composition factors of a finite nonsolvable group with these properties.

Antonov, V. A. Nozhkina, T. G.
Published in
Mathematical Notes

In the paper, the finite groups G are studied for which every invariant subgroup A has the property that |G: ACG(A)| divides a fixed prime p.

Shi, Jiangtao Zhang, Cui

We prove that any finite group having at most 27 non-normal proper subgroups of non-prime-power order is solvable except for G≅ A5, the alternating group of degree 5.

Shi, Jiangtao Zhang, Cui

We prove that any finite group having at most 27 non-normal proper subgroups of non-prime-power order is solvable except for G≅ A5, the alternating group of degree 5.

Shi, Jiangtao Zhang, Cui

We prove that any finite group having at most 27 non-normal proper subgroups of non-prime-power order is solvable except for G≅ A5, the alternating group of degree 5.

Shi, Jiangtao Zhang, Cui

We prove that any finite group having at most 27 non-normal proper subgroups of non-prime-power order is solvable except for G≅ A5, the alternating group of degree 5.