dc.contributor.author | Garrido, Alejandra | |
dc.contributor.author | Uria Albizuri, Jone | |
dc.date.accessioned | 2024-02-08T10:10:24Z | |
dc.date.available | 2024-02-08T10:10:24Z | |
dc.date.issued | 2018-12-13 | |
dc.identifier.citation | Archiv der Mathematik 112 : 123-137 (2019) | |
dc.identifier.issn | 0003-889X | |
dc.identifier.uri | http://hdl.handle.net/10810/65209 | |
dc.description.abstract | 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. | es_ES |
dc.description.sponsorship | 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. | es_ES |
dc.language.iso | eng | es_ES |
dc.publisher | Springer | es_ES |
dc.rights | info:eu-repo/semantics/openAccess | es_ES |
dc.subject | congruence subgroup property | es_ES |
dc.subject | Branch groups | es_ES |
dc.subject | profinite completion | es_ES |
dc.title | Pro-C congruence properties for groups of rooted tree automorphisms | es_ES |
dc.type | info:eu-repo/semantics/article | es_ES |
dc.rights.holder | © 2018, Springer Nature Switzerland AG | * |
dc.relation.publisherversion | https://link.springer.com/article/10.1007/s00013-018-1278-6 | |
dc.identifier.doi | /10.1007/s00013-018-1278-6 | |
dc.departamentoes | Matemáticas | es_ES |
dc.departamentoeu | Matematika | es_ES |