关于群的阶与群的共轭类数的商

On the Quotient of the Group Order and the Number of Conjugacy Classes

讨论有限群的阶与群的共轭类数之比的问题 .得到 :定理 设G为非Abel有限群 ,p为G的最小素因子 ,c1为G中非中心元素共轭类长度的最小者 ,μ(G)为群G的阶与群的共轭类个数之商 ,则 : μ(G)≥ c1p2p2 +c1- 1; 若Z(G)的阶为奇数 ,则 μ(G) =2当且仅当G/Z(G) S3 .

Let G be a finite nonabelian group, μ(G) denote the quotient of the order of G and the number of conjugacy classes of G. Assume p is the smallest prime divisor of G, and c_1 is the smallest length of conjugacy classes of G which not in Z(G), this paper proves that: (1) μ(G)≥c_1p^2p^2+c_1-1. (2) if Z(G) is odd, then μ(G)=2 if and only if G/Z(G)S_3.