The Influence Of (?)-subgroups, π-quasinormally Embedded Subgroups And (?)-subgroups On The Structure Of Finite Groups

In this paper,we study the influence of(?)-subgroups,π-quasinormally embedded subgroups and(?)-subgroups on the structure of finite groups.The main results are the following:(1)We obtain some sufficient conditions on p-nilpotency and nilpotency of finite groups under the conditions that some minimal subgroups,cyclic subgroups of order 4,subgroups of order p~2 are(?)-subgroups.Meanwhile,we get some results about certain formation;(2)We obtain some sufficient conditions on p-nilpotency of finite groups under the conditions that a nontrivial p-subgroup has a normal chain such that every main factor isπ-quasinormally embedded subgroup.(3)We define a new condition of weakly normality((?)-subgroups),give its properties, and obtain some results about p-nilpotency of finite groups.