On p-stability in groups and fusion systems

Héthelyi, L., Szőke, M. and Zalesski, A.E. (2017) On p-stability in groups and fusion systems. Journal of Algebra, 492. pp. 253-297. ISSN 0021-8693

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The aim of this paper is to generalise the notion of p-stability (p is an odd prime) in finite group theory to fusion systems. We first compare the different definitions of p-stability for groups and examine properties of p -stability concerning subgroups and factor groups. Motivated by Glauberman's theorem, we study the question of 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 Qd(p) by a cyclic group of order p. Then we define p-stability for fusion systems and characterise some of its properties. We prove a fusion theoretic version of Thompson'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. We also examine relationship between solubility and p -stability for fusion systems and determine the simple groups whose fusion systems are Qd(p)-free.

Item Type: Article
Uncontrolled Keywords: finite simple groups,simple groups of lie type,saturated fusion systems,soluble fusion systems,p-stability,qd(p)-free groups and fusion systems
Faculty \ School: Faculty of Science > School of Mathematics
UEA Research Groups: Faculty of Science > Research Groups > Algebra and Combinatorics
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Depositing User: Pure Connector
Date Deposited: 09 Sep 2017 05:06
Last Modified: 13 May 2023 00:16
URI: https://ueaeprints.uea.ac.uk/id/eprint/64802
DOI: 10.1016/j.jalgebra.2017.08.028

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