Genus actions of finite simple groups
type: Item
instance of: scholarly article
title: Genus actions of finite simple groups
zbMATH Open document ID: 0654.20013
author: Andrew J. Woldar
published in: Illinois Journal of Mathematics
publication date: 1989-01-01T00:00:00Z
review text: For integers r,s,t\(\geq 2\), consider a tessellation of the plane P by triangles having angles \(\pi\) /r, \(\pi\) /s, and \(\pi\) /t (P spherical, euclidean, or hyperbolic). Let T(r,s,t) be the group of symmetries of P preserving this tessellation. To each epimorphism \(\eta\) : T(r,s,t)\(\to G\), there corresponds a conformal action of G on the Riemann surface \(S=P/\ker \eta\). For G simple nonabelian, we show, with one exception, that G is normal in Aut(S). We further show that Aut(S) embeds in Aut G, provided G is (2,m,n)-generated and S is any surface of least genus on which G acts. Finally, for such G and S, we extend the normality result to surfaces arising from epimorphisms of the form \(\eta\) : \(\Gamma\) \(\to G\), where \(\Gamma\) is arbitrary Fuchsian.
Mathematics Subject Classification ID: 20D08
Mathematics Subject Classification ID: 20F65
Mathematics Subject Classification ID: 20F05
Mathematics Subject Classification ID: 20H10
Mathematics Subject Classification ID: 30F35
Mathematics Subject Classification ID: 20F29
zbMATH DE Number: 4067181
zbMATH Keywords: triangle group
zbMATH Keywords: Euler characteristic
zbMATH Keywords: (r,s,t)-group
zbMATH Keywords: tessellation
zbMATH Keywords: group of symmetries
zbMATH Keywords: conformal action
zbMATH Keywords: Riemann surface
zbMATH Keywords: genus
zbMATH Keywords: Fuchsian groups
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4067181