Clifford theory of characters in induced blocks

2013/10/21 by Shigeo Koshitani, Koshitani, Shigeo, Britta Spaeth +1 · 1 citation
Computer Science · Mathematics · #20C15 #20C20 #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1310.5484

openalex publication_date 2013/10/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present a new criterion to predict if a character of a finite group extends. Let G be a finite group and p a prime. For N\lhd G, we consider p-blocks b and b' of N and \rm N_N(D), respectively, with (b')^N=b, where D is a defect group of b'. Under the assumption that G coincides with a normal subgroup G[b] of G, which was introduced by Dade early 1970's, we give a character correspondence between the sets of all irreducible constituents of ϕ^G and those of (ϕ')^\rm N_G(D) where ϕ and ϕ' are irreducible Brauer characters in b and b', respectively. This implies a sort of generalization of the theorem of Harris-Knörr. An important tool is the existence of certain extensions that also helps in checking the inductive Alperin-McKay and inductive Blockwise Alperin Weight conditions, due to the second author.

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