关于有限群的弱S-可补嵌入子群(英文)

On Weakly s-supplemently Embedded Subgroups of Finite Groups

假定H是有限群G的一个子群.如果对于|H|的每个素因子p,H的一个Sylow p-子群也是G的某个s-可换子群的Sylow p-子群,则称H为G的s-可换嵌入子群;如果存在G的子群T使得G=HT并且H∩T≤HG,其中HG为群G含于H的最大的正规子群,则称H为G的c-可补子群;如果存在G的子群T使得G=HT并且H∩T≤Hse,其中Hse为群G含于H的一个s-可换嵌入子群,则称H为G的弱s-可补嵌入子群.本文研究弱s-可补嵌入子群对有限群结构的影响.某些新的结论被进一步推广.

Suppose that G is a finite group and H is a subgroup of G. H is said to be s-permutably embedded in G if for each prime p dividing ｜H｜, a Sylow p-subgroup of H is also a Sylow p-subgroup of some s-permutable subgroup of G; H is called c-supplemented in G if there exists a subgroup T of G such that G = HT and H ∩ T ≤ HG, where HG is the largest normal subgroup of G contained in H. H is said to be weakly s-supplemently embedded in G if there are a subgroup T of G and an s-permutably embedded subgroup Hse of G contained in H such that G = HT and H ∩ T ≤ Hse. We investigate the influence of weakly s-supplemently embedded subgroups on the structure of finite groups. Some recent results are generalized.