恰有两个子群共轭类长的有限群

Finite Groups with Exactly Two Conjugacy Class Sizes of Subgroups

设G是有限群,Ns(G)表示G的子群共轭类长构成的集合.本文研究Ns(G)中只有两个元素时有限群G的结构,在非幂零情形时给出了G的完全分类,在幂零情形时获得了G的一些性质.

Let G be a finite group and Ns（G） denote the set of conjugacy class sizes of all subgroups of G. The aim of this paper is to investigate the finite groups G with Ns（G） exactly having two elements. We classfy the groups for the nonuilpotent case, and also obtain some properties for the nilpotent case.