有限群的局部s置换子群(英文)

On partially s-permutable subgroups of finite groups

设G是一个有限群.群G的子群H称为在G中局部s置换,如果存在G的次正规子群T使得G=HT且H∩T≤HsT,HsT是由所有包含在H中的并与T的所有Sylow子群可置换的子群生成.利用局部s置换子群研究了有限群的结构,得到了一些关于p幂零群和p超可解群的新判别准则.

Let H be a subgroup of G.His said to be partially s-permutable in Gprovided Ghas a subnormal subgroup T such that G=HT and H ∩T≤HsT,where HsT is the subgroup of H generated by all the subgroups of H which permute with all the Sylow subgroups of T.Here,partially s-permutable subgroups were used to study the structure of finite groups and some new criteria of p-nilpotent groups and p-supersoluble groups were obtained.