Groups whose non-permutable subgroups satisfy certain conditions.

摘要

In this dissertation, we determine the structure of groups whose non-permutable subgroups satisfy certain conditions. In Chapter 1, we give the definitions and well-known results that we will use during the dissertation. In Chapter 2, we express our main result, which states that an infinite rank X -group with all proper subgroups permutable or of finite rank has all subgroups permutable. Before proving our main result in Chapter 4, we establish some preliminary results in Chapter 3 which are used in proving the main result.;In Final Chapter, we study the class of locally graded groups with all subgroups permutable or nilpotent of bounded class c. We prove that such groups are soluble of derived length bounded by a number depending on c. This chapter contains preliminary investigations into the problem of the structure of groups with all subgroups permutable or soluble.