Normal subgroups of even index in an NEC group
type: Item
instance of: scholarly article
title: Normal subgroups of even index in an NEC group
zbMATH Open document ID: 0617.20026
DOI: 10.1007/BF01194293
author: J. A. Bujalance
published in: Archiv der Mathematik
publication date: 1987-01-01T00:00:00Z
review text: We analyze normal subgroups of a NEC group \(\Gamma\) (discrete subgroup of the isometry group of the non-euclidean plane U, with compact quotient space) when the index of the subgroup with respect to the group is even. The technique we use is the study of a fundamental region for the subgroup derived from a fundamental region for the group. In Sect. 2 we give definitions and basic results. In Sect. 3 we compute the period cycles in the signature of a normal subgroup of even index in a NEC group. As a consequence of these results, in Sect. 4 we establish conditions on the signatures of the groups for a NEC group to have a normal subgroup of even index which is a surface group. This allows us to find the signatures of groups \(\Gamma\) and \(\Gamma\) ' for which \(G\cong \Gamma '/\Gamma\) is an automorphism group of even index of the Klein surface, and this to find signatures of NEC groups \(\Gamma\) for which U/\(\Gamma\) is a Klein surface having an automorphism of order 2.
Mathematics Subject Classification ID: 20H15
Mathematics Subject Classification ID: 20E07
Mathematics Subject Classification ID: 20F34
Mathematics Subject Classification ID: 30F35
zbMATH DE Number: 4000216
zbMATH Keywords: normal subgroups
zbMATH Keywords: isometry group
zbMATH Keywords: non-euclidean plane
zbMATH Keywords: fundamental region
zbMATH Keywords: subgroup of even index
zbMATH Keywords: signatures
zbMATH Keywords: surface group
zbMATH Keywords: automorphism group
zbMATH Keywords: Klein surface
zbMATH Keywords: NEC groups
MaRDI profile type: Publication
cites work: Q3658193
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full work available at URL: https://doi.org/10.1007/bf01194293
OpenAlex ID: W2078413827
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description: scientific article; zbMATH DE number 4000216