Stallings automata for free-times-abelian groups

We extend the classical Stallings theory (describing subgroups of free groups as automata) to direct products of free and abelian groups: after introducing enriched automata (i.e., automata with extra abelian labels), we obtain an explicit bijection between subgroups and a certain type of such enric...

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Autores: Delgado Rodríguez, Jordi|||0000-0002-8365-8929, Ventura, Enric|||0000-0003-3519-4135
Tipo de recurso: artículo
Fecha de publicación:2022
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:264540
Acceso en línea:https://ddd.uab.cat/record/264540
https://dx.doi.org/urn:doi:10.5565/PUBLMAT6622209
Access Level:acceso abierto
Palabra clave:Free group
Free-abelian group
Direct product
Subgroup
Intersection
Stallings
Automata
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spelling Stallings automata for free-times-abelian groupsintersections and indexDelgado Rodríguez, Jordi|||0000-0002-8365-8929Ventura, Enric|||0000-0003-3519-4135Free groupFree-abelian groupDirect productSubgroupIntersectionStallingsAutomataWe extend the classical Stallings theory (describing subgroups of free groups as automata) to direct products of free and abelian groups: after introducing enriched automata (i.e., automata with extra abelian labels), we obtain an explicit bijection between subgroups and a certain type of such enriched automata, which-as it happens in the free group-is computable in the finitely generated case. This approach provides a neat geometric description of (even non-(finitely generated)) intersections of finitely generated subgroups within this non-Howson family. In particular, we give a geometric solution to the subgroup intersection problem and the finite index problem, providing recursive bases and transversals, respectively. 22022-01-0120222022-01-01Articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://ddd.uab.cat/record/264540https://dx.doi.org/urn:doi:10.5565/PUBLMAT6622209reponame:Dipòsit Digital de Documents de la UABinstname:Universitat Autònoma de BarcelonaInglésengopen accesshttp://purl.org/coar/access_right/c_abf2Aquest material està protegit per drets d'autor i/o drets afins. Podeu utilitzar aquest material en funció del que permet la legislació de drets d'autor i drets afins d'aplicació al vostre cas. Per a d'altres usos heu d'obtenir permís del(s) titular(s) de drets.https://rightsstatements.org/vocab/InC/1.0/info:eu-repo/semantics/openAccessoai:ddd.uab.cat:2645402026-06-06T12:50:31Z
dc.title.none.fl_str_mv Stallings automata for free-times-abelian groups
intersections and index
title Stallings automata for free-times-abelian groups
spellingShingle Stallings automata for free-times-abelian groups
Delgado Rodríguez, Jordi|||0000-0002-8365-8929
Free group
Free-abelian group
Direct product
Subgroup
Intersection
Stallings
Automata
title_short Stallings automata for free-times-abelian groups
title_full Stallings automata for free-times-abelian groups
title_fullStr Stallings automata for free-times-abelian groups
title_full_unstemmed Stallings automata for free-times-abelian groups
title_sort Stallings automata for free-times-abelian groups
dc.creator.none.fl_str_mv Delgado Rodríguez, Jordi|||0000-0002-8365-8929
Ventura, Enric|||0000-0003-3519-4135
author Delgado Rodríguez, Jordi|||0000-0002-8365-8929
author_facet Delgado Rodríguez, Jordi|||0000-0002-8365-8929
Ventura, Enric|||0000-0003-3519-4135
author_role author
author2 Ventura, Enric|||0000-0003-3519-4135
author2_role author
dc.subject.none.fl_str_mv Free group
Free-abelian group
Direct product
Subgroup
Intersection
Stallings
Automata
topic Free group
Free-abelian group
Direct product
Subgroup
Intersection
Stallings
Automata
description We extend the classical Stallings theory (describing subgroups of free groups as automata) to direct products of free and abelian groups: after introducing enriched automata (i.e., automata with extra abelian labels), we obtain an explicit bijection between subgroups and a certain type of such enriched automata, which-as it happens in the free group-is computable in the finitely generated case. This approach provides a neat geometric description of (even non-(finitely generated)) intersections of finitely generated subgroups within this non-Howson family. In particular, we give a geometric solution to the subgroup intersection problem and the finite index problem, providing recursive bases and transversals, respectively.
publishDate 2022
dc.date.none.fl_str_mv 2
2022-01-01
2022
2022-01-01
dc.type.none.fl_str_mv Article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://ddd.uab.cat/record/264540
https://dx.doi.org/urn:doi:10.5565/PUBLMAT6622209
url https://ddd.uab.cat/record/264540
https://dx.doi.org/urn:doi:10.5565/PUBLMAT6622209
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
https://rightsstatements.org/vocab/InC/1.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
https://rightsstatements.org/vocab/InC/1.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:Dipòsit Digital de Documents de la UAB
instname:Universitat Autònoma de Barcelona
instname_str Universitat Autònoma de Barcelona
reponame_str Dipòsit Digital de Documents de la UAB
collection Dipòsit Digital de Documents de la UAB
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