Homomorphisms from a finite group into wreath products

Abstract

Let G be a finite group, A a finite abelian group. Each homomorphism ${\varphi:G\rightarrow A\wr S_n}$ induces a homomorphism ${\overline{\varphi}:G\rightarrow A}$ in a natural way. We show that as ${\varphi}$ is chosen randomly, then the distribution of ${\overline{\varphi}}$ is close to uniform. As application we prove a conjecture of T. Müller on the number of homomorphisms from a finite group into Weyl groups of type D _n .