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. 2023;51(3):657-683.
doi: 10.1007/s10013-023-00628-0. Epub 2023 May 10.

Strongly Base-Two Groups

Timothy C Burness  1 , Robert M Guralnick  2
Affiliations

Strongly Base-Two Groups

Timothy C Burness et al. Vietnam J Math. 2023.

Abstract

Let G be a finite group, let H be a core-free subgroup and let b(G, H) denote the base size for the action of G on G/H. Let α(G) be the number of conjugacy classes of core-free subgroups H of G with b(G,H)≥3. We say that G is a strongly base-two group if α(G)≤1, which means that almost every faithful transitive permutation representation of G has base size 2. In this paper, we study the strongly base-two finite groups with trivial Frattini subgroup.

Keywords: Bases; Finite groups; Primitive groups.

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