Automorphism groups of \(q\)-trigonal planar Klein surfaces and maximal surfaces
type: Item
instance of: scholarly article
title: Automorphism groups of \(q\)-trigonal planar Klein surfaces and maximal surfaces
zbMATH Open document ID: 1171.30016
author: B. Estrada
author: Ernesto Martínez
published in: Journal of the Mathematical Society of Japan
publication date: 2009-07-01T00:00:00Z
full work available at URL: article
review text: A Klein surface \(X\) is said to be \(q\)-trigonal if it admits an automorphism \(\varphi\) of order three such that the algebraic genus of the quotient \(X/\langle \varphi \rangle\) is equal to \(q\). A Klein surface is said to be planar if it has topological genus 0 and \(k\geq 3\) boundary components. In this paper the authors give the complete list of the automorphism groups of \(q\)-trigonal planar Klein surfaces. This result is based on careful research on the list of the automorphism groups of planar Klein surfaces presented by \textit{E. Bujalance} [Manuscr. Math. 56, 105--124 (1986; Zbl 0605.14030)]. The authors also determine the \(q\)-trigonal planar Klein surfaces which have maximal symmetry, that is, the surfaces admitting the automorphism group of maximal order \(12(k-2)\). These surfaces, called maximal surfaces, are constructed by using NEC groups, and the fundamental polygons are presented by pasting the images of the Lambert quadrilateral.
reviewed by: Gou Nakamura
Mathematics Subject Classification ID: 30F50
Mathematics Subject Classification ID: 14J50
Mathematics Subject Classification ID: 20H10
zbMATH DE Number: 5573652
zbMATH Keywords: Klein surfaces
zbMATH Keywords: NEC groups
zbMATH Keywords: automorphism groups
zbMATH Keywords: fundamental polygons
MaRDI profile type: Publication
OpenAlex ID: W2005811551
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DOI: 10.2969/JMSJ/06120607
description: scientific article; zbMATH DE number 5573652