二次极大子群中的2阶子群可补的有限群

Finite groups in whose second maximal subgroups the cyclic subgroups of order 2 are complemented

设G为有限群,H≤G,称H在G中可补。如果存在G的子群K,使得G=HK,且H∩K=1.给出了二次极大子群的2阶循环子群可补的有限非可解群的完全分类。

A subgroup H of a finite group G is called to be complemented in G if thereexist a subgroup K of G such that HK = G and H∩K = 1.In this paper,we will classifyall finite nonsolvable groups in whose second maximal subgroups the cyclic subgroups of 4 order 2 are complemented.