| Counting homomorphisms between two groups is a basic problem in group theory.Applying the structure of the generated groups and the corresponding relations between generator,we get the method to how to solve the problem of counting the number of homomorphisms between two non abelian finite groups in this paper.We also give the enumeration of homomorphisms from dihedral group and quasi-dihedral group into some non abelian groups generated by 2 elements and correct the mistakes of relative papers.As for application,we get the result that conjecture of T.Asai and T.Yoshida is satisfied on those groups. |
