Automorphism groups of compact planar Klein surfaces
type: Item
instance of: scholarly article
title: Automorphism groups of compact planar Klein surfaces
zbMATH Open document ID: 0605.14030
DOI: 10.1007/BF01171036
published in: Manuscripta Mathematica
publication date: 1986-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/155160
review text: Let \(X=D/\Gamma\) be a 2-sphere with k boundary components, and a Klein surface structure. Let G be a finite group, \(\sigma =(g,\pm,[-],\{(-)^ k\})\) the signature of an NEC-group; \(\sigma'\) the signature of another NEC-group \(\Gamma'\) and \(\theta: \Gamma'\to G\) an epimorphism. The author states some condition on \(\sigma'\) under which the following relations hold: (a) \(G\cong Aut(D/\Gamma)\) and (b) \(G\times {\mathbb{Z}}/(2)\) is an automorphism group of \(D/\ker\theta\). Using these results and the fact that all possible automorphism groups of X are also automorphism groups of the sphere he lists all the automorphism groups of X (theorem 3.1) the proof is based on some technical computational methods.
Mathematics Subject Classification ID: 14H30
Mathematics Subject Classification ID: 20H15
Mathematics Subject Classification ID: 30F40
Mathematics Subject Classification ID: 30F35
Mathematics Subject Classification ID: 20B25
Mathematics Subject Classification ID: 20F29
zbMATH DE Number: 3977158
zbMATH Keywords: Klein surface
zbMATH Keywords: NEC-group
zbMATH Keywords: automorphism groups
author: Emilio Bujalance
reviewed by: Turgut Başkan
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3977158