- Title
- Pro- C congruence properties for groups of rooted tree automorphisms
- Creator
- Garrido, Alejandra; Uria-Albizuri, Jone
- Relation
- Archiv der Mathematik Vol. 112, Issue 2, p. 123-137
- Publisher Link
- http://dx.doi.org/10.1007/s00013-018-1278-6 10.1007/s00013-018-1278-6
- Publisher
- Birkhaeuser Science
- Resource Type
- journal article
- Date
- 2019
- 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.
- Subject
- groups acting on rooted trees; weakly branch groups; congruence subgroups; profinite completions
- Identifier
- http://hdl.handle.net/1959.13/1443017
- Identifier
- uon:41861
- Identifier
- ISSN:0003-889X
- Language
- eng
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