| For a long time,using normality to study the structure of finite groups is one of the important topics of finite group theory.In this paper,some new characterizations of group properties and structures are obtained by studying the concepts related to normality.In chapter 3,we consider the finite groups all of whose maximal subgroups of even order are CBNA-gronps.Firstly,we discussed the cases where the EBNAgroup G is a 2-nilpotent group and a minimal non 2-nilpotent group,respectively.Then,we discussed the cases of |G|2>2 and |G|2=2,respectively.Finally,We discussed the cases of |π(G)|=2 and |π(G)|=3 respectively,and obtained the structure of the EBNA-group.In chapter 4,we consider the finite groups with several subnormal and selfnormal subgroups.Firstly,the structure of S-group is given,and then the supersolvability of S-group,the solvability of minimal non-S-group and the number of prime divisors of order are obtained.Finally,the complete classification of minimal non-S-group is obtained by discussing the number of prime divisors of order of minimal non S-group G and the case that G is a supersolvable group and minimal non-supersolvable group,respectively. |
