Minigulov, N. A.
Published in
Proceedings of the Steklov Institute of Mathematics

Let 𝐺\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$G$$\end{document} be a finite group. Denote by 𝜋𝐺\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{was...

Kondrat’ev, A. S. Trofimov, V. I.
Published in
Proceedings of the Steklov Institute of Mathematics

This is the fourth in a series of papers whose results imply the validity of a strong version of the Sims conjecture on finite primitive permutation groups. In this paper, the case of primitive groups with a simple socle of orthogonal Lie type and nonparabolic point stabilizer is considered. Let G be a finite group, and let M1 and M2 be distinct co...

Grechkoseeva, M. A.
Published in
Siberian Mathematical Journal

The spectrum of a finite group is the set of the orders of its elements. We consider the problem that arises within the framework of recognition of finite simple groups by spectrum: Determine all finite almost simple groups having the same spectrum as its socle. This problem was solved for all almost simple groups with exception of the case that th...

Gorshkov, I. B. Maslova, N. V.
Published in
Algebra and Logic

It is shown that the Gruenberg–Kegel graph of a finite almost simple group is equal to the Gruenberg–Kegel graph of some finite solvable group iff it does not contain 3-cocliques. Furthermore, we obtain a description of finite almost simple groups whose Gruenberg–Kegel graphs contain no 3-cocliques.

Kondrat’ev, A. S. Trofimov, V. I.
Published in
Proceedings of the Steklov Institute of Mathematics

This is the third in a series of papers whose results imply the validity of a strong version of the Sims conjecture on finite primitive permutation groups. In this paper, the case of primitive groups with simple socle of classical nonorthogonal Lie type and nonparabolic point stabilizer is considered.

Baikalov, A. A.
Published in
Algebra and Logic

It is proved that for any solvable subgroup G of an almost simple group S with simple socle isomorphic to An, n ≥ 5, there are elements x, y, z, t ∈ S such that G ∩ Gx ∩ Gy ∩ Gz ∩ Gt = 1.

Alekseeva, O. A. Kondrat’ev, A. S.
Published in
Proceedings of the Steklov Institute of Mathematics

Finite groups whose prime graphs do not contain triangles are investigated. In the present part of the study, the isomorphic types of prime graphs and estimates of the Fitting length of solvable groups are found and almost simple groups are determined.

Zinov’eva, M. R. Kondrat’ev, A. S.
Published in
Proceedings of the Steklov Institute of Mathematics

We find finite almost simple groups with prime graphs all of whose connected components are cliques, i.e., complete graphs. The proof is based on the following fact, which was obtained by the authors and is of independent interest: the prime graph of a finite simple nonabelian group contains two nonadjacent odd vertices that do not divide the order...

Kondrat’ev, A. S. Trofimov, V. I.
Published in
Proceedings of the Steklov Institute of Mathematics

This is the second in a series of papers whose results imply the validity of a strong version of the Sims conjecture on finite primitive permutation groups. In this paper, the case of primitive groups with simple socle of exceptional Lie type and nonparabolic point stabilizer is considered.

Zenkov, V. I.
Published in
Proceedings of the Steklov Institute of Mathematics

It is proved that, in a finite group G whose socle is isomorphic to Ln(2), there exist primary subgroups A and B such that the intersection of A and any subgroup conjugate to B under the action of G is nontrivial only if G is isomorphic to the group Aut(Ln(2)); in this case, A and B are 2-subgroups. All ordered pairs (A,B) of such subgroups are des...