City Research Online

Abstract

Let G be a p-solvable group, P ≤ G a p-subgroup and χ ∈ Irr(G) such that χ(1)p ≥ |G : P |p. We prove that the restriction χP is a sum of characters induced from subgroups Q ≤ P such that χ(1)p = |G : Q|p. This generalizes previous results by Giannelli–Navarro and Giannelli–Sambale on the number of linear constituents of χP . Although this statement does not hold for arbitrary groups, we conjecture a weaker version which can be seen as an extension of Brauer–Nesbitt’s theorem on characters of p-defect zero. It also extends a conjecture of Wilde.

Publication Type:	Article
Additional Information:	© 2021. This article has been published in Journal of Algebra by Elsevier. This manuscript version is made available under the CC-BY-NC-ND 4.0 license https://creativecommons.org/licenses/by-nc-nd/4.0/
Publisher Keywords:	p-solvable groups, Character restriction, Linear constituents
Subjects:	Q Science > QA Mathematics
Departments:	School of Science & Technology > Mathematics

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