Bordered and unbordered Klein surfaces with maximal symmetry
type: Item
instance of: scholarly article
title: Bordered and unbordered Klein surfaces with maximal symmetry
zbMATH Open document ID: 0595.20058
DOI: 10.1016/0022-4049(86)90057-5
author: C. Pérez-Chirinos
author: José Javier Etayo
published in: Journal of Pure and Applied Algebra
publication date: 1986-01-01T00:00:00Z
review text: An \(M^*\)-group G is a group of automorphisms of a compact Klein surface [see \textit{N. L. Alling} and \textit{N. Greenleaf}, Foundations of the theory of Klein surfaces (1971; Zbl 0225.30001)] of algebraic genus \(g\geq 2\) such that \(\| G\| =12(g-1)\), i.e. is maximal [see \textit{C. L. May}, Pac. J. Math. 59, 199-210 (1975; Zbl 0422.30037)]. In the present work the authors exhibit four new infinite families of simple \(M^*\)-groups, and determine with the aid of a computer the groups PSL(n,q) of order less than 50.000 that are \(M^*\)-groups. Using these results, the authors prove the existence of seven topologically different Klein surfaces S of algebraic genus \(g=1013\), all of them having maximal symmetry, i.e. \(\| Aut S\| =12(g-1)\).
Mathematics Subject Classification ID: 20H10
Mathematics Subject Classification ID: 30F40
Mathematics Subject Classification ID: 20F29
Mathematics Subject Classification ID: 20B25
Mathematics Subject Classification ID: 20E32
Mathematics Subject Classification ID: 30F10
zbMATH DE Number: 3957450
zbMATH Keywords: computer-aided proof
zbMATH Keywords: group of automorphisms
zbMATH Keywords: compact Klein surface
zbMATH Keywords: infinite families of simple \(M^*\)-groups
zbMATH Keywords: maximal symmetry
reviewed by: Boris N. Apanasov
MaRDI profile type: Publication
full work available at URL: 0022-4049(86)90057-5
OpenAlex ID: W2157068505
cites work: Klein surfaces and real algebraic function fields
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cites work: Large automorphism groups of compact Klein surfaces with boundary, I
cites work: The species of bordered Klein surfaces with maximal symmetry of low genus
cites work: Orientable and non-orientable Klein surfaces with maximal symmetry
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description: scientific article; zbMATH DE number 3957450