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 be the number of conjugacy classes of core-free subgroups H of G with . We say that G is a strongly base-two group if , 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.
© The Author(s) 2023.