Bounds on the number of lifts of a Brauer character in a p-solvable group

2006/05/30 by James P. Cossey, Cossey, James P.
Mathematics · #20C15 #20C20 #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT) #math.GR #math.RT #msc:20C15 #msc:20C20

paper · pdf · doi:10.48550/arxiv.math/0605772

arxiv created 2006/05/30 · arxiv updated 2009/12/01

Abstract

The Fong-Swan theorem shows that for a p-solvable group G and Brauer character ϕ∈ \ibrg, there is an ordinary character χ∈ \irrg such that χ⁰ = ϕ, where ⁰ denotes restriction to the p-regular elements of G. This still holds in the generality of π-separable groups \citebpi, where \ibrg is replaced by \ipig. For ϕ∈ \ipig, let L_ϕ = \χ∈ \irrg | χ⁰ = ϕ\. In this paper we give a lower bound for the size of L_ϕ in terms of the structure of the normal nucleus of ϕ and, if G is assumed to be odd and π= \p' \, we give an upper bound for L_ϕ in terms of the vertex subgroup for ϕ.

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• Counting lifts of Brauer characters
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• Inducing π-partial characters with a given vertex