Characters, Commutators and Centers of Sylow Subgroups
Representation Theory
2023-03-21 v2 Group Theory
Abstract
The character table of a finite group G determines whether |P:P'|=p^2 and whether |P:Z(P)|=p^2, where P is a Sylow p-subgroup of G. To prove the latter, we give a detailed classification of those groups in terms of the generalized Fitting subgroup.
Cite
@article{arxiv.2204.04407,
title = {Characters, Commutators and Centers of Sylow Subgroups},
author = {Gabriel Navarro and Benjamin Sambale},
journal= {arXiv preprint arXiv:2204.04407},
year = {2023}
}
Comments
18 pages, referee's comments incorporated