Some Generalizations Of Dedekind Groups

In this paper we investigate some generalizations of Dedekind groups.This paper consists of six chapters. Chapter I is an introduction to thispaper, consisting of background and main results. Chapter II gives a listof preliminaries for the paper. In Chapter III , we classified the groups allof whose non-normal abelian subgaoups have the same order. In ChapterVI , we classified the groups all of whose non-normal abelian subgaoupsare cyclic. In Chapter V , we discussed the groups with non-normal cyclicsubgroups possessing the same order by Magma. In Chapter VI ,we clas-sified the metacyclic groups all of whose non-normal cyclic subgroups areof order 2 or 4.