ON THE INVOLUTION FIXITY OF SIMPLE GROUPS

被引:0
作者
Burness, Timothy C. [1 ]
Covato, Elisa [1 ]
机构
[1] Univ Bristol, Sch Math, Bristol BS8 1UG, Avon, England
关键词
Primitive groups; simple groups; involution fixity; PERMUTATION-GROUPS; MAXIMAL-SUBGROUPS; ELEMENTS; FINITE;
D O I
10.1017/S0013091521000237
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Let G be a finite permutation group of degree n and let ifix(G) be the involution fixity of G, 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 T is an alternating or sporadic group; our main result classifies the groups of this form with ifix(T) <= n(4/9). This builds on earlier work of Burness and Thomas, who studied the case where T is an exceptional group of Lie type, and it strengthens the bound ifix(T) > n(1/6) (with prescribed exceptions), which was proved by Liebeck and Shalev in 2015. A similar result for classical groups will be established in a sequel.
引用
收藏
页码:408 / 426
页数:19
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