子群H称为在有限群G中有补,如果存在G的子群K使得G=HK且H∩K=1.利用某些极小子群的可补性,该文给出了有限群成为p-幂零和可解的若干充分或必要条件.一些已知的结果得到了推广.
A subgroup H is said to be complemented in a finite group G if there exists a subgroup K of G such that G =HK and H∩K = 1. In this paper, we present some sufficient and necessary conditions for a finite group to be p-nilpotent and solvable by using some complemented minimal subgroups. As applications, we extend some known results.