The number of conjugacy classes contained in normal subgroups of solvable groups

摘要

Let G be a finite group and let N be a normal subgroup of G. Assume that N is the union of ξ(N) distinct conjugacy classes of G. In this paper, we classify solvable groups G in which the set K(G) = {ξ (N)| N G, N ≠ G} has at most three elements. We also compute the set K(G) in most cases.