dc.contributor.author Garrido, A. dc.contributor.author Uria-Albizuri, J. dc.date.accessioned 2018-11-29T13:52:41Z dc.date.available 2018-11-29T13:52:41Z dc.date.issued 2018-11-21 dc.identifier.issn 0003-889X dc.identifier.uri http://hdl.handle.net/20.500.11824/894 dc.description.abstract We propose a generalisation of the congruence subgroup problem for groups acting on rooted trees. en_US Instead of only comparing the profinite completion to that given by level stabilizers, we also compare pro-$\mathcal{C}$ completions of the group, where $\mathcal{C}$ is a pseudo-variety of finite groups. A group acting on a rooted, locally finite tree has the $\mathcal{C}$-congruence subgroup property ($\mathcal{C}$-CSP) if its pro-$\mathcal{C}$ completion coincides with the completion with respect to level stabilizers. We give a sufficient condition for a weakly regular branch group to have the $\mathcal{C}$-CSP. In the case where $\mathcal{C}$ 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. dc.format application/pdf en_US dc.language.iso eng en_US dc.rights Reconocimiento-NoComercial-CompartirIgual 3.0 España en_US dc.rights.uri http://creativecommons.org/licenses/by-nc-sa/3.0/es/ en_US dc.title Pro-C congruence properties for groups of rooted tree automorphisms en_US dc.type info:eu-repo/semantics/article en_US dc.relation.projectID EUS/BERC/BERC.2018-2021 en_US dc.relation.projectID EUS/BERC/BERC.2014-2017 en_US dc.rights.accessRights info:eu-repo/semantics/openAccess en_US dc.type.hasVersion info:eu-repo/semantics/acceptedVersion en_US dc.journal.title Archiv der Mathematik en_US
﻿

### This item appears in the following Collection(s)

Except where otherwise noted, this item's license is described as Reconocimiento-NoComercial-CompartirIgual 3.0 España