关于弱s-可补子群的几个定理

Some Theorems on Weakly s-supplemented Subgroups

称群G的一个子群H在G中是弱s-可补的,如果存在G的一个子群K,使得G=HK且H∩K≤HsG,其中HsG是包含在H中的G的最大的s-置换子群.利用弱s-可补子群研究有限群的结构,推广了前人的一些结果.

A subgroup H of a group G is said to be weakly s-supplemented in G if there exists a subgroup K of G such that G=HK and H∩K≤HsG,Where HsG is the maximal s-permutable subgroup of G contained in H.We investigate the structure of finite groups by using weakly s-supplemented subgroups.Some recent results are generalized.