Several Types Of Locally Nilpotent P-group

The aim of this thesis is to study locally nilpotent p- groups by using some theory of finite p- groups.The main results of this thesis are in Chapter 2,3,4.In chapter 2,we study the p-automorphism of divisible abelian groups of rank p-1 and p.In[5],it showed that a divisible abelian groups D has p-automorphism iff the of rank D is greater than p-1.Here we get the order of the p-automorphism groups of the divisible abelian groups of rank p-1 and p.We also investigate how p-automorphism groups act on the divisible abelian groups.This research can help us to understand the structure of(?)ernikov p-groups.In chapter 3,we show that the characteristic subgroupsΩ_n(G) and(?)_n(G) have strong influence on the structure of locally nilpotent p-group G.We study the structure of locally nilpotent p-groups G with |G:(?)_n(G)|＜∞,which are generalization of Baumslag.G[10]and Cernikov.S.N[11,12].Furthermore,we investigate locally nilpotent p-groups G with |Ω₁(G)|≤p² or |Ω₂(G)|=p³.In chapter 4,we try to generalize the theory of finite regular p-groups in locally nilpotent p-groups.Infinite regular p-groups with |G:(?)_n(G)|＜∞and some infinite irregular p-groups whose proper factor groups or proper infinite subgroups are regular are investigated in this chapter.