Influences Of Subgroups Of Prime Power On The Structure Of Finite Groups

The thesis focuses on the S-qusinormality, C-normality, completely C*-permutability and S-semipermutability of subgroups of prime power of a finite group and aims at studying their influences on the structure of a finite group, such as supersolvability, p-nilpotency, and p-solvability, etc. On the basis of these discussions, we get some interesting results. The body of this thesis, in accordance with the research focuses, is divided into four chapters.The first is concerned with the theoretical and practical backgroud informations for the current research.The second is to investigate the relationship between the S-qusinormal1ity and C-normality of subgroups of prime power and the structure of the corresponding finite group. The influences of S-qusinormality and C-normality of subgroups of prime power on the structure of a finite group have been studied by a long series of papers and the research has been continued. In combination of the concepts of S-quasinormal subgroup and C-normal subgroup, some sufficient conditions are obtained for finite groups to be surpersolvable.In chapter three, we first advances a new concept, an completely C*-permutable subproup of a finite group, and explores its inheritance of a subgroup and a quotient group. Moreover, the paper discusses the sufficient conditions of p-nilpotency and supersolvability of a finite group and extends some of them to a formation.In the literature [27], professor Li first introduce the followingDefinition: Let d be the smallest generator number of a p-group P. We consider the set M_d(P) = {P₁,…, Pd} of all elements of M(P) such that∩_i=1^d P_i = (?)(P), where M(P) is the set of all maxmal subgroups of P.He investigate the structure of a finite group G by means of the members of M_d(G_p) for all primes p, where G_p∈Syl_p(G).At last chapter, we follow this tradition and continue studying the structure of a finite group from the point of view of Md(G_p).