四元数群到一类亚循环群之间的同态个数

The number of homomorphisms from the Quaternion group into 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,具体地计算出四元数群到一类亚循环群之间的同态个数.

We use the basic properties of group theorem and number theory to calculate the number of homomorphisms from the Quaternion group into a class of metacyclic groups, which are normal cyclic groups of the order n extended by cyclic groups of the order 4.