两类非交换群之间的同态数量

Number of homomorphisms between two classes of non-abelian finite groups

结合代数数论的知识,计算了一类Sylow p-子群为循环群的10pn阶非交换群之间的同态个数,以及这类群到四元数群的同态个数。作为应用,验证了这两类群是满足Asai和Yoshida猜想的。

The number of homomorphisms among a class of non-abelian groups of order 10pn with cyclic Sylow p-subgroups and from the non-abelian finite groups into quaternion group is obtained by using algebraic number theory.As an application,the number of homomorphisms of such groups satisfies the conjecture of Asai and Yoshida is verified.