p-Basilica Groups

We consider a generalisation of the Basilica group to all odd primes: the p-Basilica groups acting on the p-adic tree. We show that the p-Basilica groups have the p-congruence subgroup property but not the congruence subgroup property nor the weak congruence subgroup property. This provides the firs...

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Autores: Di Domenico, Elena, Fernández Alcober, Gustavo Adolfo, Noce, MariaLaura, Thillaisundaram, Anitha
Tipo de recurso: artículo
Fecha de publicación:2022
País:España
Institución:Universidad del País Vasco
Repositorio:Addi. Archivo Digital para la Docencia y la Investigación
OAI Identifier:oai:addi.ehu.eus:10810/59375
Acceso en línea:http://hdl.handle.net/10810/59375
Access Level:acceso abierto
Palabra clave:groups acting on rooted trees
weakly branch groups
congruence subgroup properties
Hausdorff dimension
maximal subgroups
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spelling p-Basilica GroupsDi Domenico, ElenaFernández Alcober, Gustavo AdolfoNoce, MariaLauraThillaisundaram, Anithagroups acting on rooted treesweakly branch groupscongruence subgroup propertiesHausdorff dimensionmaximal subgroupsWe consider a generalisation of the Basilica group to all odd primes: the p-Basilica groups acting on the p-adic tree. We show that the p-Basilica groups have the p-congruence subgroup property but not the congruence subgroup property nor the weak congruence subgroup property. This provides the first examples of weakly branch groups with such properties. In addition, the p-Basilica groups give the first examples of weakly branch, but not branch, groups which are super strongly fractal. We compute the orders of the congruence quotients of these groups, which enable us to determine the Hausdorff dimensions of the p-Basilica groups. Lastly, we show that the p-Basilica groups do not possess maximal subgroups of infinite index and that they have infinitely many non-normal maximal subgroups.Open access funding provided by Università degli Studi di Salerno within the CRUI-CARE Agreement.Springer202320232022info:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10810/59375reponame:Addi. Archivo Digital para la Docencia y la Investigacióninstname:Universidad del País VascoIngléshttps://link.springer.com/article/10.1007/s00009-022-02187-zinfo:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by/3.0/es/© The Author(s) 2022. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.Atribución 3.0 Españaoai:addi.ehu.eus:10810/593752026-06-18T09:23:17Z
dc.title.none.fl_str_mv p-Basilica Groups
title p-Basilica Groups
spellingShingle p-Basilica Groups
Di Domenico, Elena
groups acting on rooted trees
weakly branch groups
congruence subgroup properties
Hausdorff dimension
maximal subgroups
title_short p-Basilica Groups
title_full p-Basilica Groups
title_fullStr p-Basilica Groups
title_full_unstemmed p-Basilica Groups
title_sort p-Basilica Groups
dc.creator.none.fl_str_mv Di Domenico, Elena
Fernández Alcober, Gustavo Adolfo
Noce, MariaLaura
Thillaisundaram, Anitha
author Di Domenico, Elena
author_facet Di Domenico, Elena
Fernández Alcober, Gustavo Adolfo
Noce, MariaLaura
Thillaisundaram, Anitha
author_role author
author2 Fernández Alcober, Gustavo Adolfo
Noce, MariaLaura
Thillaisundaram, Anitha
author2_role author
author
author
dc.subject.none.fl_str_mv groups acting on rooted trees
weakly branch groups
congruence subgroup properties
Hausdorff dimension
maximal subgroups
topic groups acting on rooted trees
weakly branch groups
congruence subgroup properties
Hausdorff dimension
maximal subgroups
description We consider a generalisation of the Basilica group to all odd primes: the p-Basilica groups acting on the p-adic tree. We show that the p-Basilica groups have the p-congruence subgroup property but not the congruence subgroup property nor the weak congruence subgroup property. This provides the first examples of weakly branch groups with such properties. In addition, the p-Basilica groups give the first examples of weakly branch, but not branch, groups which are super strongly fractal. We compute the orders of the congruence quotients of these groups, which enable us to determine the Hausdorff dimensions of the p-Basilica groups. Lastly, we show that the p-Basilica groups do not possess maximal subgroups of infinite index and that they have infinitely many non-normal maximal subgroups.
publishDate 2022
dc.date.none.fl_str_mv 2022
2023
2023
dc.type.none.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv http://hdl.handle.net/10810/59375
url http://hdl.handle.net/10810/59375
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/s00009-022-02187-z
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by/3.0/es/
Atribución 3.0 España
eu_rights_str_mv openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by/3.0/es/
Atribución 3.0 España
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
_version_ 1869411680463618048
score 15,300719

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