二面体群到一类亚循环群之间的同态个数

The number of homomorphisms from dihedral groups to a class of metacyclic groups

基于群理论中亚循环群的结构以及该群元素的特征,利用代数学及数论的基本方法,具体地计算出二面体群到一类亚循环群之间的同态个数。作为应用,验证了 T. Asai 和 T. Yoshdia 猜想对此类亚循环群成立。

Based on the theory group of the structure of metacyclic group and characteristics of the group elements, by using the basic method of algebra and number theory, it is calculated that the number of homomorphism between dihedral groups and a class of metacyclic groups. As an application, it verifies that T.Asai and T.Yoshidas' conjectures establish such a cyclic group.