具有很多素数阶元的有限群

FINITE GROUPS WITH MANY ELEMENTS OF PRIME ORDER

考察元素的阶如何影响有限群的结构是群论中的一个重要课题 .本文研究存在一个正规子群 N,N外的元素都是素数阶元的有阶群 .主要利用熟知的 Thompson的一个定理 ,获得了这样的有限群 .

To investigate how element orders influence the structure of a finite group is an important subject in group theory. The aim of this paper is to investigate the structure of a finite group which possesses a normal subgroup N such that all elements outside N are of prime order. Mainly by a well-known theorem of Thompson, we obtain such a group.