Divisibility results on the number of conjugacy classes in finite groups

摘要

1.Terminology and history. Throughout this paper G is a finite group, N a normal subgroup, and H an arbitrary subgroup. We denote the center of G by Z and the intersection of H with the centralizer of g by CH(g). The set of conjugacy classes of G is denoted e/(G), and cl(g) means the conjugacy class of g in G. The number of conjugacy classes of a group G is denoted kG.