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 .
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Schlage-Puchta, JC. Homomorphisms from a finite group into wreath products. Arch. Math. 96, 27–30 (2011). https://doi.org/10.1007/s00013-010-0188-z
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DOI: https://doi.org/10.1007/s00013-010-0188-z