The Influence Of Completely Conditionally Permutability And Semi Cover-avoiding Properties Of Subgroups On The Structure Of Finite Groups

In this paper, we study the relationship between, the structure of finite groups and thecompletely conditionally permutability and semi cover-avoiding properties of some subgroups.The main results are the following:(1) We obtain some sufficient conditions on p-nilpotency of finite groups by using thecompletely conditionally permutability of some minimal subgroups, cyclic subgroups of order4, subgroups of order p~2. Meanwhile, we get some results about certain formation;(2) We obtain some sufficient conditions on p-nilpotency of finite groups by using thesemi cover-avoiding properties of some minimal subgroups, cyclic subgroups of order 4, max-imal subgroups of Sylow subgroups and 2-maximal subgroups of Sylow subgroups. Mean-while, we get some results about certain formation.