Homomorphisms from a finite group into wreath products

摘要

Let G be a finite group, A a finite abelian group. Each homomorphism j:G® Awr S_n{varphi:Grightarrow Awr S_n} induces a homomorphism [`(j)]:G® A{overline{varphi}:Grightarrow A} in a natural way. We show that as j{varphi} is chosen randomly, then the distribution of [`(j)]{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 .