The Influence Of Elements Of The Maximal Order And Weakly S-Semipermutable Properties Of Subgroups On The Structure Of Finite Groups

In this paper, we study the relationship between the structure of finite groups and the elements of the maximal order and weakly s-semipermutable properties of some subgroups. The main results are the following:(1) Let p is prime, m is a positive integer, G is a finite group, if |M(G)| = 6p~m. then G is solvable group.Let p > 5, p is prime, m, t is non-negative integers, G is a finite group, if |M(G)| = 2·5~m·p~t. then G is solvable group,(2) We obtain some sufficient conditions on p-nilpotency of finite groups by using the weakly s-semipermutable properties of some minimal subgroups, cyclic subgroups of order 4, subgroups of order p2. Meanwhile, we get some results about certain formation;...