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Zbl 0923.20002
Glasby, S.P.; Kovács, L.G.
Irreducible modules and normal subgroups of prime index. (English)
[J] Commun. Algebra 24, No.4, 1529-1546 (1996). ISSN 0092-7872; ISSN 1532-4125

Summary: Let $\bbfF$ be a field, $G$ a finite group, $H$ a normal subgroup of prime index $p$, and $V$ an irreducible $\bbfF H$-module. If $\bbfF$ is algebraically closed and of characteristic $0$, the $\bbfF G$-module induced from $V$ is either irreducible or a direct sum of $p$ pairwise nonisomorphic irreducible modules. It is shown here that if $\bbfF$ is not assumed algebraically closed and its characteristic is not $0$, then there are not two but six possibilities for the structure of the induced module.

MSC 2000:: *20C05 Group rings of finite groups and their modules (group theory)
20C20 Modular representations and characters of groups

Keywords: finite groups; normal subgroups; irreducible modules; induced modules

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