一类内交换p-群与四元数群之间的同态个数

Number of homomorphisms between intra-commutative p-groups and quaternion groups

根据内交换p-群和四元数群的结构特征以及元素的性质,计算了一类内交换p-群和四元数群之间的同态个数,并验证了T.Asai和T.Yoshida猜想对此类群成立。

Based on the group structure and element properties of intra-commutative p-groups and quaternion groups, the number of homomorphisms from a class of intra-commutative p-groups into quaternion groups is calculated. As an application, the conjecture of T.Asai and T.Yoshida is proved to be valid for such groups.