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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.