关键词: 群同态, 群作用, 自由交换群

Abstract:

Let $G$ be a finite group, and $F=F_{r} \times A$ be a finitely generated Abelian group, where $A$ is finite and $F_{r}$ is a free Abelian group of rank $r$. It is proved that the number of homomorphisms from $F$ to $G$ is a multiple of $|A|$ and $|G|$ greatest common divisor. The results generalize the famous T.Yoshdia theorem.

Key words: group homomorphism, group action, free Abelian group