Restrictions of characters in p-solvable groups

authored by

Damiano Rossi, Benjamin Sambale

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 χ

_P 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 χ

_P. 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.

Organisation(s)

Institute of Algebra, Number Theory and Discrete Mathematics

External Organisation(s)

The University of Wuppertal

Type

Article

Journal

Journal of algebra

Volume

587

Pages

130-141

No. of pages

12

ISSN

0021-8693

Publication date

01.12.2021

Publication status

Published

Peer reviewed

Yes

ASJC Scopus subject areas

Algebra and Number Theory

Electronic version(s)

https://arxiv.org/abs/2106.04818 (Access: Open)
https://doi.org/10.1016/j.jalgebra.2021.07.034 (Access: Closed)