Study On The Number Of Endomorphisms And Automorphisms Of The 2qp~n Order Groups

The discussion and characterization of the number of homomorphisms of finite groups is an important problem in the study of group theory,which can classify finite groups indirectly.Based on the structure and generation relation of known groups,we use the classification of the order of 2qpn(q<p and odd prime)groups,where Sylow p-subgroup is a cyclic group in isomorphism in this paper.Combined with the knowledge of group theory and number theory,the number of endomorphisms and automorphisms of such 2qpn groups and the number of group homomorphisms between them are calculated by constructing the image of generators of each class of groups under homomorphic mapping.Based on the number of homomorphisms obtained above,it is verified that such 2qpn groups satisfy the conjecture of T.Asai&T.Yoshida.