摘要
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.
出处
《数学进展》
CSCD
北大核心
2012年第3期373-383,共11页
Advances in Mathematics(China)
基金
supported by NSFC(No.11171243,No.10871032)
the Natural Science Foundation of Jiangsu Province(No.BK2008156)
Guangdong Province(No.S2011010004447)
关键词
弱s-可补嵌入子群
超可解群
P-幂零群
饱和群系
weakly s-supplemently embedded subgroup
supersolvable group
p-nilpotent group
saturated formation