Real genus 12
type: Item
instance of: scholarly article
title: Real genus 12
zbMATH Open document ID: 1082.30035
author: Beata Mockiewicz
published in: Rocky Mountain Journal of Mathematics
publication date: 2005-03-10T00:00:00Z
review text: Let \(G\) be a finite group. The real genus of \(G\) is the minimum algebraic genus of any compact bordered Klein surface on which \(G\) acts as a group of automorphisms. \textit{C. L. May} has proved that for infinitely many integers \(p>2\) there exist groups of the real genus \(p\) but no group of the real genus 2 [Rocky Mt. J. Math. 23, No. 2, 707--724 (1993; Zbl 0795.30039)]. Then we have a question whether there is \(p>2\) such that there exists no group of the real genus \(p\). In this paper the author shows that there exists no group of the real genus 12. A group \(G\) is represented by a factor group \(\Lambda/\Gamma\) of two NEC groups \(\Lambda\) and \(\Gamma\), where \(\Gamma\) is a bordered surface group normalizing a Klein surface. Considering the signatures of \(\Lambda\) and the presentations of \(G\), the author gets the result.
reviewed by: Gou Nakamura
Mathematics Subject Classification ID: 30F50
Mathematics Subject Classification ID: 14H45
Mathematics Subject Classification ID: 20F05
Mathematics Subject Classification ID: 20H10
Mathematics Subject Classification ID: 57M60
zbMATH DE Number: 2143234
zbMATH Keywords: real genus
zbMATH Keywords: Klein surface
zbMATH Keywords: NEC group
zbMATH Keywords: group of automorphisms
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1216/rmjm/1181069807
OpenAlex ID: W2034604876
cites work: Foundations of the theory of Klein surfaces
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cites work: THERE IS A GROUP OF EVERY STRONG SYMMETRIC GENUS
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DOI: 10.1216/RMJM/1181069807
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description: scientific article; zbMATH DE number 2143234