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Restrictions of characters in p-solvable groups

Rossi, D. ORCID: 0000-0003-2832-2477 & Sambale, B. (2021). Restrictions of characters in p-solvable groups. Journal of Algebra, 587, doi: 10.1016/j.jalgebra.2021.07.034

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 Mathematics, Computer Science & Engineering > Mathematics
[img] Text - Accepted Version
This document is not freely accessible until 19 August 2022 due to copyright restrictions.
Available under License Creative Commons Attribution Non-commercial No Derivatives.

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