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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2012, Volume 18, Number 3, Pages 139–143 (Mi timm847)  
This article is cited in 5 scientific papers (total 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
Full-text PDF (145 kB) Citations (5)
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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.
Received: 11.03.2012
English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2013, Volume 283, Issue 1, Pages 86–90
DOI: https://doi.org/10.1134/S0081543813090083
Bibliographic databases:
Document Type: Article
UDC: 512.542
Language: Russian
Citation: A. S. Kondrat'ev, I. V. Khramtsov, “The complete reducibility of some $GF(2)A_7$-modules”, Trudy Inst. Mat. i Mekh. UrO RAN, 18, no. 3, 2012, 139–143; Proc. Steklov Inst. Math. (Suppl.), 283, suppl. 1 (2013), 86–90
Citation in format AMSBIB
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\jour Proc. Steklov Inst. Math. (Suppl.)
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\pages 86--90
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    • This publication is cited in the following 5 articles:
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