【摘要】 群G的子群H称为半置换的,若对任意的K≤G,只要(|H|,|K|)=1,就有HK=KH.H称为s-半置换的,若对任意的p||G|,只要(p,|H|)=1,就有PH=HP,其中P∈Syl_p(G).本文利用sylow子群的2-极大子群的s-半置换性得到有限群为p-幂零群的一些充分条件.更多还原

【Abstract】 Let G be a finite group.A subgroup H of a group G is called semipermutable if it is permutable with every subgroup K of G with(|H|,|K|)=1,and s-semipermutable if it is permutable with eyery Sylow p-subgroup of G with(p,|H|)=1.The influence of s-semipermutablity of 2-maximal subgroups of Sylow subgroup of a finite group on its p-nilpotence are investigated.更多还原