Representations induced from a normal subgroup of prime index

2018/10/06 by Soham Swadhin Pradhan, Pradhan, Soham Swadhin
Mathematics · #Finite Group Theory Research

paper · pdf · doi:10.48550/arxiv.1810.05084

Abstract

Let G be a finite group, H be a normal subgroup of prime index p. Let F be a field of either characteristic 0 or prime to |G|. Let η be an irreducible F-representation of H. If F is an algebraically closed field of characteristic either 0 or prime to |G|, then the induced representation η\uparrow^G_H is either irreducible or a direct sum of p pairwise inequivalent irreducible representations. In this paper, we show that if F is not assumed algebraically closed field, then there are five possibilities in the decomposition of induced representation into irreducible representations.

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