On p-stability in groups and fusion systems

On p-stability in groups and fusion systems

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 cyc...

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Veröffentlicht in:arXiv.org 2017-01
Hauptverfasser: Héthelyi, László, Szőke, Magdolna, Zalesski, Alexandre
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Stability
Subgroups
Theorems
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Szőke, Magdolna
Zalesski, Alexandre
description 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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title On p-stability in groups and fusion systems
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