有限生成交换群到有限群间的同态数量

Number of homomorphisms between finitely generated Abelian groups and finite groups

设G为有限群,F=A×Fr为有限生成交换群,其中A是有限的,Fr为自由交换群,证明F到G的同态数量是|A|与|G|最大公因子的倍数,推广著名的T.Yoshdia定理。

Let G be a finite group,and F=Fr×A be a finitely generated Abelian group,where A is finite and Fr 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.