一类非交换内循环群到有限群的同态个数

Number of Homomorphisms from a Class of Non Commutative Inner Cyclic Groups to Finite Groups

首先,利用群论和同余理论计算一类非交换内循环群的自同态个数和自同构个数,并给出该类内循环群到一般有限群同态个数满足的数量关系;其次,验证上述情形的数量关系对Asai和Yoshida猜想成立.

Firstly,by using group theory and congruence theory,the author calculated the number of endomorphisms and automorphisms between a class of non commutative inner cyclic groups,and gave the quantity relation of the number of homomorphisms from such inner cyclic groups to finite groups.Secondly,the author verified that the conjectures of Asai and Yoshida were true for the above cases.