LA-Group And The Stractore Of Auto-Morphism Groups Of Some Special P-Groups

In this dissertation, we main research some news LA-groups and the structure of Auto-morphism groups of some special p -groups . By using the method of free groups, this is to say, generators and dinfining relations and extension theorem analyze some new series LA-groups. The existence of those groups is proved by using the method of extension theorem and free groups, which are in accidence with the LA-conjecture. The structure of Auto-morphism groups of some special p -groups is analysised by the method of holomorph and semi-direct product. The main results are as follows:Chapter One. We introduce the backgrounds and the current investigation of in this thesis.Chapter Two. The analysis of some series new LA-groups. At the beginning, we assume some new din fining relations by the dinfining relations of |G|=p~4, and prove property of conjecture groups, we obtain its structure andexistence by free groups . At last, we obtain all those groups are LA -Groups bymeans of the results of automorphism groupChapter Three. Let G be a finite p-group, |G| = p~5. The characteristic of the precise structure of the auto-morphism groups of groups of order p~5, which have cyclic and maximal subgroups, is analysised by the method of holomorph and semi-direct product. At the same time, we show that the groups with these properties are LA-groups. It also has real values to the absolute solution of the famous LA- conjecture.