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arXiv · 1701.02008

On p-stability in groups and fusion systems

László Héthelyi·Magdolna Szőke·Alexandre Zalesski
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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.

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László Héthelyi, Magdolna Szőke, Alexandre Zalesski. 2017-01-08. On p-stability in groups and fusion systems. https://arxiv.org/abs/1701.02008

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