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## A generating function of the number of homomorphisms from a surface group into a finite
group

## Published Web Location

https://arxiv.org/pdf/math/0209008.pdfNo data is associated with this publication.

## Abstract

A generating function of the number of homomorphisms from the fundamental group of a compact oriented or non-orientable surface without boundary into a finite group is obtained in terms of an integral over a real group algebra. We calculate the number of homomorphisms using the decomposition of the group algebra into irreducible factors. This gives a new proof of the classical formulas of Frobenius, Schur, and Mednykh.