Properties of Certain Classes of Finite Groups

Abstract

In this thesis only finite groups are considered. A group G is said to be a T0 -group if every subnormal subgroup of Gjif!(G) is normal in G/if!(G), where if!(G) stands for the Frattini subgroup (the intersection of all maximal subgroups) of G. The principal

aim of this thesis is twofold:

1- To determine the structure of a group G all of its proper sub­

groups are T0 -groups.

2- To study the structure of a group G under the assumption . that certain subgroups of prime power order are well-situated in G.

This thesis includes six Chapters:

CHAPTER I. This Chapter is concerned with establishing the notation and the basic definitions that will be used throughout the thesis.

CHAPTER II. We list a nurriber of well known results which will be used throughout the thesis, referring the reader• to their proofs in the literature. \Ve also prove some of the easier ones that• are used often in the thesis.