Archiv der Mathematik

, Volume 96, Issue 1, pp 27–30

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 Dn.

Mathematics Subject Classification (2000)

20P05 20E22 

Keywords

Wreath products Homomorphism numbers Weyl groups 

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References

  1. 1.
    Müller T.: Enumerating representations in finite wreath products. Adv. Math. 153, 118–154 (2000)MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Müller T., Schlage-Puchta J.-C.: Classification and Statistics of Finite Index Subgroups in Free Products. Adv. Math. 188, 1–50 (2004)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Müller T., Schlage-Puchta J.-C.: Statistics of Isomorphism types in free products. Adv. Math. 224, 707–720 (2010)MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Basel AG 2010

Authors and Affiliations

  1. 1.GentBelgium

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