有限群的m-S-可补子群

Finite groups with some m-S-supplemented subgroups

令G是一个有限群。群G的子群S称为在G中是m-S-置换的,如果存在着G的模子群A和S-置换子群B使得S=〈A,B〉。群G的子群H称为在G中是m-S-可补的,如果存在着G的m-S-置换子群S和G的子群T使得G=HT且H∩T≤S≤H。通过研究m-S-可补子群对有限群结构的影响,得到了有限群的p-幂零性和超可解性的一些新的判别准则,并推广了一些已得到的结果。

Let G be a finite group. A subgroup S of G is said to be m-S-permutable in G,if S =〈A,B〉for some modular subgroup A and S-permutable subgroup B of G. A subgroup H of G is said to be m-S-supplemented in G,if there are an m-S-permutable subgroup S and a subgroup T of G such that G = HT and H ∩T≤S≤H. By using the m-S-supplemented subgroups to characterize the structure of finite groups. Some new characterizations of p-nilpotency and supersolubility of finite groups are obtained and generalize some known results.