四元数群到一类10p^n阶非交换群的同态数量

Number of Homomorphisms from Quaternion Group toa Class of Non-Abelian Groups with Order 10p^n

利用有限群论和初等数论确定一类10p^n阶非交换群的元素特征,并构建四元数群到该类10p^n阶非交换群的所有同态映射.通过计算这些同态映射的个数,验证这两类群满足Asai和Yoshida猜想.

By using the finite group theory and elementary number theory,we ascertained the characteristics of elements of a class of non-Abelian finite group with order 10p^n,and built all homomorphic mappings from quaternion group to the class of non-Abelian finite group with order 10p^n.We verified that those two groups could suffice the conjecture of Asai and Yoshida by calculating the number of homomorphic mapping.