Restrictions of characters in p-solvable groups
Representation Theory
2021-07-23 v2 Group Theory
Abstract
Let G be a p-solvable group, P a p-subgroup and chi in Irr(G) such that chi(1)_p \ge |G:P|_p. We prove that the restriction chi_P is a sum of characters induced from subgroups Q\le P such that chi(1)_p=|G:Q|_p. This generalizes previous results by Giannelli--Navarro and Giannelli--Sambale on the number of linear constituents of chi_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.
Keywords
Cite
@article{arxiv.2106.04818,
title = {Restrictions of characters in p-solvable groups},
author = {Damiano Rossi and Benjamin Sambale},
journal= {arXiv preprint arXiv:2106.04818},
year = {2021}
}
Comments
10 pages, conjecture modified since the original conjecture was false