The maximal finite subgroup in the mapping class group of genus 5
type: Item
instance of: scholarly article
title: The maximal finite subgroup in the mapping class group of genus 5
zbMATH Open document ID: 0906.14017
author: B. Battsengel
published in: Proceedings of the Japan Academy. Series A
publication date: 1997-05-14T00:00:00Z
review text: The highest order of the group of automorphisms of compact Riemann surfaces of genus five is 192. The Riemann surface which realizes the maximum is unique and is realized as the modular curve \(X(8)\) of level 8 [see \textit{A. Kuribayashi} and \textit{H. Kimura}, J. Algebra 134, No. 1, 80-103 (1990; Zbl 0709.30037)]. The author of this note gives the action of the group of automorphisms of \(X(8)\) on a set of generators of its fundamental group and determines a set of canonical generators.
Mathematics Subject Classification ID: 14H55
Mathematics Subject Classification ID: 14H30
Mathematics Subject Classification ID: 14H37
Mathematics Subject Classification ID: 30F10
zbMATH DE Number: 993530
zbMATH Keywords: Riemann surfaces
zbMATH Keywords: fundamental groups
reviewed by: A. Del Centina
MaRDI profile type: Publication
full work available at URL: pjaa.72.141
OpenAlex ID: W2026345667
cites work: The Nielsen realization problem
cites work: Automorphism groups of compact Riemann surfaces of genus five
cites work: Q5568135
cites work: PARABOLIC POINTS AND ZETA-FUNCTIONS OF MODULAR CURVES
cites work: Q4239097
DOI: 10.3792/PJAA.72.141
description: scientific article; zbMATH DE number 993530