The full group of automorphisms of non-orientable unbordered Klein surfaces of topological genus 6
type: Item
instance of: scholarly article
title: The full group of automorphisms of non-orientable unbordered Klein surfaces of topological genus 6
zbMATH Open document ID: 1390.57009
author: Adrián Bacelo
published in: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM
publication date: 2018-04-12T00:00:00Z
review text: Non-orientable unbordered Klein surfaces are the non-orientable versions of compact Riemann surfaces. The groups which occur as the full automorphism groups of non-orientable Klein surfaces are known up to genus 5, and in the present paper the author gives such a classification for genus 6 (in a sequel to the present paper, [\textit{A. Bacelo}, Rev. Mat. Complut. 31, No. 1, 247--261 (2018; Zbl 1383.57024)], he obtained a classification also for genus 7). A basic concept here is the \textit{symmetric crosscap number} of a finite group which is defined as the minimum genus of an unbordered non-orientable Klein surface on which the group acts, and basic for the present paper are the known groups of crosscap number up to 6 (there are 11 groups of symmetric crosscap number 6; by computer-algebra methods, Conder classified the groups of symmetric crosscap number up to 65, publishing the results on his homepage).
Mathematics Subject Classification ID: 57M60
Mathematics Subject Classification ID: 30F50
zbMATH DE Number: 6859079
zbMATH Keywords: non-orientable Klein surface
zbMATH Keywords: automorphism group
reviewed by: Bruno Zimmermann
MaRDI profile type: Publication
full work available at URL: s13398-017-0387-6
OpenAlex ID: W2592307873
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DOI: 10.1007/S13398-017-0387-6
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description: scientific article; zbMATH DE number 6859079