On the divisibility of $#\Hom(\Gamma,G)$ by $|G|
  We extend and reformulate a result of Solomon on the divisibility of the title. We show, for example, that if $\Gamma$ is a finitely generated group, then $|G|$ divides $#\Hom(\Gamma,G)$ for every finite group $G$ if and only if $\Gamma$ has infinite abelianization. As a consequence we obtain some arithmetic properties of the number of subgroups of a given index in such a group $\Gamma$. 
Fernando Rodriguez Villegas and Cameron Gordon
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