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.

Liu, Yufeng Guo, Wenbin Kovaleva, V. A. Skiba, A. N.
Published in
Mathematical Notes

Let A, K, and H be subgroups of a group G and K ≤ H. Then we say that A covers the pair (K, H) if AH = AK and avoids the pair (K, H) if A ∩ H = A ∩ K. A pair (K, H) in G is said to be maximal if K is a maximal subgroup of H. In the present paper, we study finite groups in which some subgroups cover or avoid distinguished systems of maximal pairs of...

Li, Xianhua Zhang, Xinjian
Published in
Siberian Mathematical Journal

Under study is the influence of the index of H in 〈H,Hg〉 for g ∈ G on the structure of a group G, where H is either a second maximal subgroup of G or a Sylow subgroup of G.

Dashkova, O. Yu.
Published in
Siberian Advances in Mathematics

Let A be an RG-module over a commutative ring R, where G is a group of infinite section p-rank (0-rank), CG(A) = 1, A is not a Noetherian R-module, and the quotient A/CA(H) is a Noetherian R-module for every proper subgroup H of infinite section p-rank (0-rank). We describe the structure of solvable groups G of this type.

Azarov, D. N.
Published in
Mathematical Notes

A necessary and sufficient condition for the residual finiteness of a (generalized) free product of two residually finite solvable-by-finite minimax groups with cyclic amalgamated subgroups is obtained. This generalizes the well-known Dyer theorem claiming that every free product of two polycyclic-by-finite groups with cyclic amalgamated subgroups ...

Kovaleva, V. A. Skiba, A. N.
Published in
Siberian Mathematical Journal

We describe the finite solvable groups with all n-maximal subgroups \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathfrak{U}$$\end{document}-subnormal.

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

A subgroup H of a finite group G is called ℙ2-subnormal whenever there exists a subgroup chain H = H0 ≤ H1 ≤ ... ≤ Hn = G such that |Hi+1: Hi| divides prime squares for all i. We study a finite group G = AB on assuming that A and B are solvable subgroups and the indices of subgroups in the chains joining A and B with the group divide prime squares....