关于最大G-共轭类长的数量性质

On the Arithmetical Property About the Two Longest G-Conjugacy Class Sizes

设N是有限群G的一个正规子群,假设m,n是N的两个最长的非中心G-共轭类长.在m,n满足(m,n)=1且它们均无平方因子的条件下,对N的结构作了一定的描述,得到了N是一个超可解群.

Let N be a normal subgroup of a finite group G ,and the integers m and n be the two longest G‐conjugacy classes of N .This paper describes the structure of N and proves that N is a supersoluble group under the condition that both m and n are square free and coprime .