The Homomorphic Quantity Research Between A Class Of Noncommutative And Modular Groups

Study the homomorphism between the two group of number problem is one of the basic problems in algebra.The study of noncommutative finite group homomorphism related to solve an equation problem in a group,that is the solution of equation in a finite group equal to the number of cyclic group homomorphism between finite group number.In this paper,by using group theory and the basic ways of number theory,specifically constructed modular group and a kind of cyclic group by cyclic group expansion of the homomorphism between cyclic group,calculating the number of the homomorphism between them,As a concrete application of homomorphic quantity,it is verified that subcyclic group and modular group satisfy T.Asai & T.Yoshida conjecture.