Morphisms Some Results

Based on previous work, this paper continues to study the morphic endomorphism on group and properties of morphic group.This paper is composed of four parts. In the first and second part, we introduce the basic conception of morphic endomorphism and morphic group, then we also discuss some properties of morphic endomorphism, and show that the composite of morphic endomorphisms need not be morphic. But the composite of automorphism and morphic endomorphism is morphic, and we give some examples of morphic group.In chapter3, we describe the structure of morphic group,and discuss the situation that groups with unique principal series or unique composition series to be morphic group.In chapter4, we investigate the influence of a kind of special endomorphism on the structure of finite groups, namely endomorphism without fixed point.