Homomorphisms from a finite group into wreath products

Details Homomorphisms from a finite group into wreath products Homomorphisms from a finite group into wreath products

2011-05-06

arxiv.org/abs/1105.1301v1

Arch. Math. (Basel) 96 (2011), no. 1, 27-30

Mathematics

Group Theory

Scientific paper

10.1007/s00013-010-0188-z

Let $G$ be a finite group, $A$ a finite abelian group. Each homomorphism $\phi:G\to A\wr S_n$ induces a homomorphism $\bar{\phi}:G\to A$ in a natural way. We show that as $\phi$ is chosen randomly, then the distribution of $\bar{\phi}$ is close to uniform. As application we prove a conjecture of T. M\"uller on the number of homomorphisms from a finite group into Weyl groups of type $D_n$.

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