Representing \(PSL_ 2(p)\) on a Riemann surface of least genus
type: Item
instance of: scholarly article
title: Representing \(PSL_ 2(p)\) on a Riemann surface of least genus
zbMATH Open document ID: 0594.30046
author: Henry H. Glover
author: Denis Sjerve
published in: L'Enseignement Mathématique. 2e Série
publication date: 1985-01-01T00:00:00Z
review text: For any finite group G denote by genus (G) the least genus of all Riemann surfaces S for which there exists an effective conformal action \(G\times S\to S\). We note that genus(G) has also been called the symmetric genus of G in the literature on combinatorial theory. This notion is closely related to the Cayley genus of a group but did not coincide with it. For details see [\textit{T. Tucker}, J. Comb. Theory, Ser. B 34, 82-92 (1983; Zbl 0521.05027)]. The purpose of the present paper is to determine the genus for the simple groups PSL\({}_ 2(p)\), where p is a prime \(\geq 5\). One of the most important steps in the proof of the main theorem of this paper is the following result. Let S be a surface of minimal genus for \(G=PSL_ 2(p)\). Then the orbit manifold S/G is the two-sphere \(S^ 2\) and the quotient map \(S\to S^ 2=S/G\) is a branched covering with exactly 3 branch points.
Mathematics Subject Classification ID: 30F35
Mathematics Subject Classification ID: 20H10
Mathematics Subject Classification ID: 20F65
zbMATH DE Number: 3955357
zbMATH Keywords: Cayley genus of a group
zbMATH Keywords: \(PSL_ 2(p)\)
zbMATH Keywords: branched covering
reviewed by: Alexander Mednykh
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3955357