RUS  ENG
Full version
JOURNALS // Trudy Instituta Matematiki i Mekhaniki UrO RAN // Archive

Trudy Inst. Mat. i Mekh. UrO RAN, 2012 Volume 18, Number 3, Pages 139–143 (Mi timm847)

This article is cited in 5 papers

The complete reducibility of some $GF(2)A_7$-modules

A. S. Kondrat'evab, I. V. Khramtsova

a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
b Ural Federal University

Abstract: It is proved that, if $G$ is a finite group with a nontrivial normal $2$-subgroup $Q$ such that $G/Q\cong A_7$ and an element of order $5$ from $G$ acts without fixed points on $Q$, then the extension of $G$ by $Q$ is splittable, $Q$ is an elementary abelian group, and $Q$ is the direct product of minimal normal subgroups of $G$ each of which is isomorphic, as a $G/Q$-module, to one of the two $4$-dimensional irreducible $GF(2)A_7$-modules that are conjugate with respect to an outer automorphism of the group $A_7$.

Keywords: finite group, $GF(2)A_7$-module, completely reducible representation, prime graph.

UDC: 512.542

Received: 11.03.2012


 English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2013, 283, suppl. 1, 86–90

Bibliographic databases:


© Steklov Math. Inst. of RAS, 2024