Free subgroups of the parametrized modular group

We study free subgroups of index four of the parametrized modular group Π, the subgroup of SL(2; Z[ξ]) generated by (10 ξ1) and (01 -10). There are eight free subgroups, four of which are normal and four are non-normal. Then we study the intersections of the normal subgroups. We give canonical prese...

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Autores:
Pommerenke, Christian
Toro, Margarita
Tipo de recurso:
Article of journal
Fecha de publicación:
2015
Institución:
Universidad Nacional de Colombia
Repositorio:
Universidad Nacional de Colombia
Idioma:
spa
OAI Identifier:
oai:repositorio.unal.edu.co:unal/66461
Acceso en línea:
https://repositorio.unal.edu.co/handle/unal/66461
http://bdigital.unal.edu.co/67489/
Palabra clave:
51 Matemáticas / Mathematics
Parametrized modular group
free subgroups
Bianchi groups
Picard group
discrete relativity theory
Rights
openAccess
License
Atribución-NoComercial 4.0 Internacional
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oai_identifier_str oai:repositorio.unal.edu.co:unal/66461
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spelling Atribución-NoComercial 4.0 InternacionalDerechos reservados - Universidad Nacional de Colombiahttp://creativecommons.org/licenses/by-nc/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Pommerenke, Christian4999ea34-cb26-4530-bec3-81efd88b32c5300Toro, Margarita41238712-8669-499d-bf35-cf4a7ab2dc503002019-07-03T02:10:19Z2019-07-03T02:10:19Z2015-07-01ISSN: 2357-4100https://repositorio.unal.edu.co/handle/unal/66461http://bdigital.unal.edu.co/67489/We study free subgroups of index four of the parametrized modular group Π, the subgroup of SL(2; Z[ξ]) generated by (10 ξ1) and (01 -10). There are eight free subgroups, four of which are normal and four are non-normal. Then we study the intersections of the normal subgroups. We give canonical presentations in terms of generators and relations. At the end of the paper we study connections between and the Bianchi groups, the two-parabolic group and a group from relativity theory.application/pdfspaUniversidad Nacional de Colombia - Sede Bogotá - Facultad de Ciencias - Departamento de Matemáticas - Sociedad Colombiana de Matemáticashttps://revistas.unal.edu.co/index.php/recolma/article/view/60445Universidad Nacional de Colombia Revistas electrónicas UN Revista Colombiana de MatemáticasRevista Colombiana de MatemáticasPommerenke, Christian and Toro, Margarita (2015) Free subgroups of the parametrized modular group. Revista Colombiana de Matemáticas, 49 (2). pp. 269-279. ISSN 2357-410051 Matemáticas / MathematicsParametrized modular groupfree subgroupsBianchi groupsPicard groupdiscrete relativity theoryFree subgroups of the parametrized modular groupArtículo de revistainfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1http://purl.org/coar/version/c_970fb48d4fbd8a85Texthttp://purl.org/redcol/resource_type/ARTORIGINAL60445-307346-1-SM.pdfapplication/pdf418146https://repositorio.unal.edu.co/bitstream/unal/66461/1/60445-307346-1-SM.pdfeb97fc00872579ffe988b7514ef53085MD51THUMBNAIL60445-307346-1-SM.pdf.jpg60445-307346-1-SM.pdf.jpgGenerated Thumbnailimage/jpeg4844https://repositorio.unal.edu.co/bitstream/unal/66461/2/60445-307346-1-SM.pdf.jpg9caac7ea69144aa51dbd8e5bbcd7ad43MD52unal/66461oai:repositorio.unal.edu.co:unal/664612023-05-25 23:02:47.685Repositorio Institucional Universidad Nacional de Colombiarepositorio_nal@unal.edu.co
dc.title.spa.fl_str_mv Free subgroups of the parametrized modular group
title Free subgroups of the parametrized modular group
spellingShingle Free subgroups of the parametrized modular group
51 Matemáticas / Mathematics
Parametrized modular group
free subgroups
Bianchi groups
Picard group
discrete relativity theory
title_short Free subgroups of the parametrized modular group
title_full Free subgroups of the parametrized modular group
title_fullStr Free subgroups of the parametrized modular group
title_full_unstemmed Free subgroups of the parametrized modular group
title_sort Free subgroups of the parametrized modular group
dc.creator.fl_str_mv Pommerenke, Christian
Toro, Margarita
dc.contributor.author.spa.fl_str_mv Pommerenke, Christian
Toro, Margarita
dc.subject.ddc.spa.fl_str_mv 51 Matemáticas / Mathematics
topic 51 Matemáticas / Mathematics
Parametrized modular group
free subgroups
Bianchi groups
Picard group
discrete relativity theory
dc.subject.proposal.spa.fl_str_mv Parametrized modular group
free subgroups
Bianchi groups
Picard group
discrete relativity theory
description We study free subgroups of index four of the parametrized modular group Π, the subgroup of SL(2; Z[ξ]) generated by (10 ξ1) and (01 -10). There are eight free subgroups, four of which are normal and four are non-normal. Then we study the intersections of the normal subgroups. We give canonical presentations in terms of generators and relations. At the end of the paper we study connections between and the Bianchi groups, the two-parabolic group and a group from relativity theory.
publishDate 2015
dc.date.issued.spa.fl_str_mv 2015-07-01
dc.date.accessioned.spa.fl_str_mv 2019-07-03T02:10:19Z
dc.date.available.spa.fl_str_mv 2019-07-03T02:10:19Z
dc.type.spa.fl_str_mv Artículo de revista
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dc.identifier.issn.spa.fl_str_mv ISSN: 2357-4100
dc.identifier.uri.none.fl_str_mv https://repositorio.unal.edu.co/handle/unal/66461
dc.identifier.eprints.spa.fl_str_mv http://bdigital.unal.edu.co/67489/
identifier_str_mv ISSN: 2357-4100
url https://repositorio.unal.edu.co/handle/unal/66461
http://bdigital.unal.edu.co/67489/
dc.language.iso.spa.fl_str_mv spa
language spa
dc.relation.spa.fl_str_mv https://revistas.unal.edu.co/index.php/recolma/article/view/60445
dc.relation.ispartof.spa.fl_str_mv Universidad Nacional de Colombia Revistas electrónicas UN Revista Colombiana de Matemáticas
Revista Colombiana de Matemáticas
dc.relation.references.spa.fl_str_mv Pommerenke, Christian and Toro, Margarita (2015) Free subgroups of the parametrized modular group. Revista Colombiana de Matemáticas, 49 (2). pp. 269-279. ISSN 2357-4100
dc.rights.spa.fl_str_mv Derechos reservados - Universidad Nacional de Colombia
dc.rights.coar.fl_str_mv http://purl.org/coar/access_right/c_abf2
dc.rights.license.spa.fl_str_mv Atribución-NoComercial 4.0 Internacional
dc.rights.uri.spa.fl_str_mv http://creativecommons.org/licenses/by-nc/4.0/
dc.rights.accessrights.spa.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv Atribución-NoComercial 4.0 Internacional
Derechos reservados - Universidad Nacional de Colombia
http://creativecommons.org/licenses/by-nc/4.0/
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.mimetype.spa.fl_str_mv application/pdf
dc.publisher.spa.fl_str_mv Universidad Nacional de Colombia - Sede Bogotá - Facultad de Ciencias - Departamento de Matemáticas - Sociedad Colombiana de Matemáticas
institution Universidad Nacional de Colombia
bitstream.url.fl_str_mv https://repositorio.unal.edu.co/bitstream/unal/66461/1/60445-307346-1-SM.pdf
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