半覆盖-远离及X-半置换子群与有限群的p-幂零性

摘要

Let H be a normal subgroup of a finite group G such that G/H is p-nilpotent and let P be a Sylow p-subgroup of H.If NG（P） is p-nilpotent and one of the following holds,then G is p-nilpotent：（1） Every maximal subgroup of P is either semi-cover-avoiding or Fp（H）-semipermutable in G;（2） Every 2-maximal subgroup of P is either semi-cover-avoiding or Fp（H）-semipermutable in G.%设H是有限群G的正规子群使得G/H为p-幂零群,P是H的一个Sylowp-子群.若NG（P）为p-幂零群且下列条件之一成立,则G是p-幂零群：（1）P的极大子群在G中半覆盖-远离或Fp（H）-半置换;（2）P的二次极大子群在G中半覆盖-远离或Fp（H）-半置换.