Research On The Congruence Of The Number Of Group Homomorphisms Between Certain Groups

Counting number of homomorphisms between groups is one of the basic probl-ems in the group theory.This paper explores the number of group homomorphisms from quaternion group to quaternion group,from quaternion group to dihedral group,from quaternion group to quasi-dihedral group,from quaternion group to modular group.This paper corrects errors in the article which is written by Rajkumar,meanwhile,proves those groups satisfying T.Asai & T.Yoshida guess.