On p-nilpotent Groups and Metabelian Groups;

Weakly C-normal Subgroups and p-nilpotent Groups;

In this paper, we study the structure of finite group G by using of the quasinormality of subgroups, condition and obtain some sufficient conditions for a group belonging to p-nilpotent groups and p-superslovable 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.

C-supplement subgroups are used to study the p-nilpotency of finite group and obtain two sufficient conditions of p-nilpotent group of finite group.

2,we consider some abelian subgroups whose centralizers are equal to its normalizers,so we obtain some sufficient conditions of p-nilpotent groups and p-closed group.

By use of the s-conditonal permutability of certain 2-maximal subgroups of Sylow subgroups,the sufficient conditions which enable a finite group to be ap-nilpotent group are obtained;some of the known theorems are further generalized.

In this paper,it is obtained that some necessary and sufficient conditions for p-nilpotent groups by means of the quasi-c-normality of some subgroups of a group G.

This paper assumes that every non-cyclic Sylow subgroup P of G has a subgroup D such that 1<|D|<|P| and all subgroups H of P with order |H|=|D| and with 2|D|(if P is a non-abelian 2-group and |P:D|>2) are normally embedded in G,and some sufficient conditions are obtained on G to be p-nilpotent groups and supersolvable groups.

Some Sufficient Conditions of p-nilpotent Groups and p-closed Groups;

Let G be a nilpotent p-group with finite rank, a andβbe two p-auto-morphisms of G, and write I = <(αβ(g))(βα(g))-1)|g∈G>, then (i) In case I is a finite cyclic group, a andβgenerate a finite p-group.