On the involution fixity of simple groups

Burness, Timothy C.; Covato, Elisa

Abstract

Let be a finite permutation group of degree and let be the involution fixity of, which is the maximum number of fixed points of an involution. In this paper, we study the involution fixity of almost simple primitive groups whose socle is an alternating or sporadic group; our main result classifies the groups of this form with. This builds on earlier work of Burness and Thomas, who studied the case where is an exceptional group of Lie type, and it strengthens the bound n (with prescribed exceptions), which was proved by Liebeck and Shalev in 2015. A similar result for classical groups will be established in a sequel.

• Journal Article Type: Article
• Acceptance Date: May 10, 2021
• Online Publication Date: May 31, 2021
• Publication Date: May 31, 2021
• Deposit Date: Apr 25, 2024
• Journal: Proceedings of the Edinburgh Mathematical Society
• Print ISSN: 0013-0915
• Electronic ISSN: 1464-3839
• Publisher: Cambridge University Press (CUP)
• Peer Reviewed: Peer Reviewed
• Volume: 64
• Issue: 2
• Pages: 408-426
• DOI: https://doi.org/10.1017/S0013091521000237
• Public URL: https://uwe-repository.worktribe.com/output/11915418