Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-11-29T08:20:51.391Z Has data issue: false hasContentIssue false
  • English
  • Français

Multi-GGS Groups have the Congruence Subgroup Property

Part of: Structure and classification of infinite or finite groups

Published online by Cambridge University Press:  21 February 2019

Alejandra Garrido  and
Jone Uria–Albizuri
Alejandra Garrido
Affiliation:
School of Mathematical and Physical Sciences, University of Newcastle, University Drive, Callaghan, NSW 2308, Australia ([email protected])
Jone Uria–Albizuri
Affiliation:
Basque Center of Applied Mathematics, Mazarredo, 14, 48009, Bilbao, Basque Country, Spain ([email protected])
Get access Rights & Permissions [Opens in a new window]

Abstract

We generalize the result about the congruence subgroup property for GGS groups in [3] to the family of multi-GGS groups; that is, all multi-GGS groups except the one defined by the constant vector have the congruence subgroup property. New arguments are provided to produce this more general proof.

Keywords

groups acting on rooted treesbranch groupscongruence subgroup propertyprofinite completion

MSC classification

Primary: 20E08: Groups acting on trees
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 62 , Issue 3 , August 2019 , pp. 889 - 894
Copyright
Copyright © Edinburgh Mathematical Society 2019 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Alexoudas, T., Klopsch, B. and Thillaisundaram, A., Maximal subgroups of multi-edge spinal groups, Groups Geom. Dyn. 10 (2016), 619–648.Google Scholar
2Fernández-Alcober, G. A. and Zugadi-Reizabal, A., GGS-groups: order of congruence quotients and Hausdorff dimension, Trans. Amer. Math. Soc. 366 (2014), 1993–2007.Google Scholar
3Fernández-Alcober, G. A., Garrido, A. and Uria-Albizuri, J., On the congruence subgroup property for GGS-groups, Proc. Amer. Math. Soc. 145 (2017), 3311–3322.Google Scholar
4Grigorchuk, R. I., On Burnside's problem on periodic groups, Funktsional. Anal. i Prilozhen. 14(1) (1980), 53–54.Google Scholar
5Gupta, N. and Sidki, S. N., On the Burnside problem for periodic groups,Math. Z. 182 (1983), 385–388.Google Scholar