On compact Riemann surfaces with a maximal number of automorphisms
type: Item
instance of: scholarly article
title: On compact Riemann surfaces with a maximal number of automorphisms
zbMATH Open document ID: 0795.30035
DOI: 10.1007/BF03026541
published in: Manuscripta Mathematica
publication date: 1994-02-07T00:00:00Z
full work available at URL: https://eudml.org/doc/155863
review text: A finite group \(G\) is a Hurwitz group if it acts as a group of automorphisms on a compact Riemann surface \(X\) of genus \(g\) and has maximal possible order \(84(g- 1)\). As such it is a quotient of the Fuchsian triangle group \((0;2,3,7)\) so that \(X/G\) has genus zero. The author introduces the notion of a genus 1 Hurwitz group with the same maximality property but subject to the restriction that \(X/G\) has genus 1. As such, \(G\) has order \(4(g-1)\) and is a quotient of the Fuchsian group of signature \((1;2)\). On a large subclass of the class of all finite groups, simple necessary and sufficient conditions are obtained for a group to be a genus 1 Hurwitz group in which case, the quotient of genus 1 can be shown to have prescribed \(j\)-invariant.
Mathematics Subject Classification ID: 30F10
zbMATH DE Number: 492795
zbMATH Keywords: automorphism group
zbMATH Keywords: Hurwitz group
author: Peter Turbek
reviewed by: C. Maclachlan
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 492795