有限群的PF-可补充子群

摘要

设A是G的子群,称A在G中是PF-可补充的,如果存在G的子群T和C≤A使得G=A T且T∩A=T∩C,其中C在G中是F-拟置换的.运用极小阶反例法,研究PF-可补充子群对有限群超可解性、幂零性的影响.利用G p(p为奇数)的每个极小子群在G中是PU-可补充的,得到G是2'-超可解的充分条件.%Let A be a subgroup of G .Then we say A is PF-supplemented in G .If G has subgroups T and C (G= A T ,T∩ A= T∩C) ,C is F-quasipermutable in G .The influence of PF-supplemented subgroups on supersolvability and nipotency of finite group is investigated by using the method of minimal counterexample .Since every minimal subgroup of Gp ( p is an odd ) is PF-supplemented in G , G is the sufficient condition for 2'-super solvable .