Groups of automorphisms of hyperelliptic Klein surfaces of genus three
type: Item
instance of: scholarly article
title: Groups of automorphisms of hyperelliptic Klein surfaces of genus three
zbMATH Open document ID: 0594.20043
published in: Michigan Mathematical Journal
publication date: 1986-01-01T00:00:00Z
review text: The order of a group of automorphisms of a compact Klein surface of genus 3 with boundary does not exceed 24 [see \textit{C. L. May}, Pac. J. Math. 59, 199-210 (1975; Zbl 0422.30037)]. These groups of automorphisms are quotients of NEC groups of isometries of the hyperbolic plane since the Klein surface may be represented as the quotient of the hyperbolic plane by an NEC group. Being hyperelliptic places certain restrictions on the possible signatures of the corresponding NEC groups. By an exhaustive search starting with the finite groups of order less than 24 and using a variety of structural results on NEC groups (several proved in earlier papers by one or more of these authors) those finite groups which can occur as the full group of automorphisms of a hyperelliptic Klein surface of genus 3 are precisely determined. The fullness is exhibited by a simple argument on dimensions of Teichmüller spaces.
Mathematics Subject Classification ID: 20H15
Mathematics Subject Classification ID: 14H30
Mathematics Subject Classification ID: 14L30
Mathematics Subject Classification ID: 20F29
zbMATH DE Number: 3955229
zbMATH Keywords: group of automorphisms of a compact Klein surface of genus 3
zbMATH Keywords: quotients of NEC groups
zbMATH Keywords: isometries of the hyperbolic plane
zbMATH Keywords: Teichmüller spaces
author: Emilio Bujalance
author: José Javier Etayo
author: Jose Manuel Gamboa
reviewed by: C. Maclachlan
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1307/mmj/1029003290
OpenAlex ID: W1998934319
DOI: 10.1307/MMJ/1029003290
description: scientific article; zbMATH DE number 3955229