非交换子群共轭类的一个注记

A note on conjugacy classes of non-abelian subgroup

设G是有限群.用τ(G)表示G中非交换子群的共轭类数,π(G)表示G的素因子的集合.对于每个非交换群有τ(G)≥2|π(G)|-2或|π(G)|+1.分析上述不等式中等号成立的有限群的分类.

Let G be a finite group and τ（G）denote the number of conjugacy classes of all non-abelian subgroups of G.The symbol π（G） denotes the set of the prime divisors of G.In which paper,Finite groups with few non-abelian subgroups,shows τ（G） ≥2 ｜π（G）｜-2 or lπ（G） ｜ ＋ 1 for every non-abelian group G,and determines the classification of the finite groups when an equality holds in the above-mentioned inequalities.