有限群可解与群的阶

Solvability and the order of a finite group

对有限群可解与群的阶进行了讨论。得到的主要结果是:设S是非交换单群的阶的集合,对于正整数n,如果存在s∈S,使s整除n,则存在不可解的n阶群。如果对于任意的s∈S,均有s不整除n,则这样的n阶群是可解群。

This paper discusses the solvability and order of a finite group and gets the following main results. Let S be the set of orders of nocommutative simple finite groups, the group G with order n exists if ←E s∈S such that sin; the group G with order n is solvable if A↓ s∈S, s n.