Archiv der Mathematik

, Volume 96, Issue 1, pp 27–30

Homomorphisms from a finite group into wreath products



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 


Wreath products Homomorphism numbers Weyl groups 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  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

Personalised recommendations