, Volume 96, Issue 1, pp 27-30
Date: 04 Dec 2010

Homomorphisms from a finite group into wreath products

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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 .