On p-stability in groups and fusion systems
Group Theory
2017-01-10 v1
Abstract
The aim of this paper is to generalise the notion of p-stability to fusion systems. We study the question how Qd(p) is involved in finite simple groups. We show that with a single exception a simple group involving Qd(p) has a subgroup isomorphic to either Qd(p) or a central extension of it by a cyclic group of order p. We define p-stability for fusion systems, characterise some of its properties and prove a fusion theoretic version of Thomson's maximal subgroup theorem. We introduce the notion of section p-stability both for groups and fusion systems and prove a version of Glauberman's theorem to fusion systems.
Cite
@article{arxiv.1701.02008,
title = {On p-stability in groups and fusion systems},
author = {László Héthelyi and Magdolna Szőke and Alexandre Zalesski},
journal= {arXiv preprint arXiv:1701.02008},
year = {2017}
}