Pro-C congruence properties for groups of rooted tree automorphisms

We propose a generalisation of the congruence subgroup problem for groups acting on rooted trees. Instead of only comparing the profinite completion to that given by level stabilizers, we also compare pro-C completions of the group, where C is a pseudo-variety of finite groups. A group acting on a r...

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Detalles Bibliográficos
Autores: Garrido, Alejandra, Uria Albizuri, Jone
Tipo de recurso: artículo
Fecha de publicación:2018
País:España
Institución:Universidad del País Vasco
Repositorio:Addi. Archivo Digital para la Docencia y la Investigación
OAI Identifier:oai:addi.ehu.eus:10810/65209
Acceso en línea:http://hdl.handle.net/10810/65209
Access Level:acceso abierto
Palabra clave:congruence subgroup property
Branch groups
profinite completion
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spelling Pro-C congruence properties for groups of rooted tree automorphismsGarrido, AlejandraUria Albizuri, Jonecongruence subgroup propertyBranch groupsprofinite completionWe propose a generalisation of the congruence subgroup problem for groups acting on rooted trees. Instead of only comparing the profinite completion to that given by level stabilizers, we also compare pro-C completions of the group, where C is a pseudo-variety of finite groups. A group acting on a rooted, locally finite tree has the C-congruence subgroup property (C-CSP) if its pro-C completion coincides with the completion with respect to level stabilizers. We give a sufficient condition for a weakly regular branch group to have the C-CSP. In the case where C is also closed under extensions (for instance the class of all finite p-groups for some prime p), our sufficient condition is also necessary. We apply the criterion to show that the Basilica group and the GGS-groups with constant defining vector (odd prime relatives of the Basilica group) have the p-CSP.A. Garrido was supported by the Alexander von Humboldt Foundation. J. Uria-Albizuri acknowledges financial support from the Spanish Government, grant MTM2014-53810-C2-2-P, and from the Basque Government, grant IT974-16 and the predoctoral grant PRE-2014-1-347. This research is also supported by the Basque Government through the BERC 2018-2021 program and by the Spanish Ministry of Science, Innovation and Universities: BCAM Severo Ochoa accreditation SEV-2017-0718.Springer202420242018info:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10810/65209reponame:Addi. Archivo Digital para la Docencia y la Investigacióninstname:Universidad del País VascoIngléshttps://link.springer.com/article/10.1007/s00013-018-1278-6info:eu-repo/semantics/openAccess© 2018, Springer Nature Switzerland AGoai:addi.ehu.eus:10810/652092026-06-18T09:23:17Z
dc.title.none.fl_str_mv Pro-C congruence properties for groups of rooted tree automorphisms
title Pro-C congruence properties for groups of rooted tree automorphisms
spellingShingle Pro-C congruence properties for groups of rooted tree automorphisms
Garrido, Alejandra
congruence subgroup property
Branch groups
profinite completion
title_short Pro-C congruence properties for groups of rooted tree automorphisms
title_full Pro-C congruence properties for groups of rooted tree automorphisms
title_fullStr Pro-C congruence properties for groups of rooted tree automorphisms
title_full_unstemmed Pro-C congruence properties for groups of rooted tree automorphisms
title_sort Pro-C congruence properties for groups of rooted tree automorphisms
dc.creator.none.fl_str_mv Garrido, Alejandra
Uria Albizuri, Jone
author Garrido, Alejandra
author_facet Garrido, Alejandra
Uria Albizuri, Jone
author_role author
author2 Uria Albizuri, Jone
author2_role author
dc.subject.none.fl_str_mv congruence subgroup property
Branch groups
profinite completion
topic congruence subgroup property
Branch groups
profinite completion
description We propose a generalisation of the congruence subgroup problem for groups acting on rooted trees. Instead of only comparing the profinite completion to that given by level stabilizers, we also compare pro-C completions of the group, where C is a pseudo-variety of finite groups. A group acting on a rooted, locally finite tree has the C-congruence subgroup property (C-CSP) if its pro-C completion coincides with the completion with respect to level stabilizers. We give a sufficient condition for a weakly regular branch group to have the C-CSP. In the case where C is also closed under extensions (for instance the class of all finite p-groups for some prime p), our sufficient condition is also necessary. We apply the criterion to show that the Basilica group and the GGS-groups with constant defining vector (odd prime relatives of the Basilica group) have the p-CSP.
publishDate 2018
dc.date.none.fl_str_mv 2018
2024
2024
dc.type.none.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv http://hdl.handle.net/10810/65209
url http://hdl.handle.net/10810/65209
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv https://link.springer.com/article/10.1007/s00013-018-1278-6
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
© 2018, Springer Nature Switzerland AG
eu_rights_str_mv openAccess
rights_invalid_str_mv © 2018, Springer Nature Switzerland AG
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
dc.source.none.fl_str_mv reponame:Addi. Archivo Digital para la Docencia y la Investigación
instname:Universidad del País Vasco
instname_str Universidad del País Vasco
reponame_str Addi. Archivo Digital para la Docencia y la Investigación
collection Addi. Archivo Digital para la Docencia y la Investigación
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,300719

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