Finite P-groups Covered By Its Minimal Nonabelian Subgroups

Suppose that,p is a prime and G is a finite p-group.We say G is covered by its minimal nonabelian subgroups if G is the union of its minimal nonabelian subgroups.What finite groups can be covered by proper subgroups?Many group theorists pay their attention on the problem,and a lot of important results have been obtained.It is known that non-p-groups can not be generated by its minimal nonabelian subgroups.However,a finite p-group is generated by its minimal nonabelian subgroups.So in a sense,minimal nonabelian subgroups can be regarded as "basic elements" of finite p-groups,which play an important role in the study of the structure of finite p-group.Therefore,it is necessary to study the question on a finite p-group covered by its minimal nonabelian subgroups.Up to now,there is no results about t.lie problem.The aiin in this thesis is to begin the study on the problem.This thesis consists of 4 chapt ers.Chapter Ⅰ is an introduction.Chapter Ⅱ gives a.list of preliminaries.In chapter Ⅲ.it is given that some sufficient.conditions and necessary conditions for a finite p-group t,o be covered by its minimal nonabelian subgroups.As application,in chapter Ⅳ,based on the classification of A2-groups and A3-groups,it,is de-termined that A2-groups and A3-groups covered by their minimal nonabelian subgroups,respectively.