Strictly C*-Normal Subgroups And The Structure Of Finite Groups

By mainly observing the c*-normality of subgroups, we introduce the concepts of strictly c*-normal subgroup and strictly C*N- group and study the solvability, p-solvability and p-nilpotency of finite groups.In Chapter one, we give the reasons why we introduce the new concepts, and list some basic concepts and important results,which are frequently used in the study of finite groups.In Chapter two, we mainly study the influence of strictly c*-normal subgroups on the solvability of finite groups.We introduce the concept of strictly c*-normal subgroups and, by using this new characteristics on some maximal, 2-maximal and Hall subgroups, we obtain several new criteria on the solvability and the -solvability of finite groups.In Chapter three, we mainly study the structure of strictly C*N-groups and obtain some sufficient and necessary conditions for a group to be a strictly C*N-group.In Chapter four, we define the conjugate graph of a finite group G. we get some graph-theoretic properties of the conjugate graphs of dihedral groups. As applications,we give some group-theoretic properties of finite groups.