【摘要】 群G的子群H称为G的弱s-拟正规子群,若G有次正规子群T,使得G=HT且H∩T≤HsG,其中HsG是包含在H中的G的最大的s-拟正规子群.本文利用Sylowp-子群的极大子群的弱s-拟正规性得到有限群为p-幂零群的一些充分条件,并给出Schur-Zassenhaus定理的一种推广.更多还原

【Abstract】 Let G be a finite group. A subgroup H of G is called weakly s-permutable in G if G has asubnormal subgroup T such that G = HT and T ∩ H ≤ HsG, where HsG is the largest s-quasinormal subgroupof G contained in H. The influence of weakly s-permutablity of maximal subgroups of Sylow subgroup of a finitegroup on its p-nilpotency are investigated. A generalization of Schur-Zassenhaus theorem is given in the paper.更多还原