On the Basilica operation

Petschick JM, Rajeev K (2023)
Groups, Geometry, and Dynamics 17(1): 331-384.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Petschick, Jan Moritz; Rajeev, KarthikaUniBi
Abstract / Bemerkung
Inspired by the Basilica group B, we describe a general construction which allows us to associate to any group of automorphisms G < Aut(T ) of a rooted tree T a family of Basilica groups Bass(G), s E NC. For the dyadic odometer O2, one has B = Bas2(O2). We study which properties of groups acting on rooted trees are preserved under this operation. Introducing some techniques for handling Bass(G), in case G fulfills some branching conditions, we are able to calculate the Hausdorff dimension of the Basilica groups associated to certain GGS-groups and of generalisations of the odometer, Odm. Furthermore, we study the structure of groups of type Bass(Odm) and prove an analogue of the congruence subgroup property in the case m = p, a prime.
Stichworte
Basilica group; groups acting on rooted trees; automatic groups; spinal; groups; Hausdorff dimension; congruence subgroup property; self-similar; groups
Erscheinungsjahr
2023
Zeitschriftentitel
Groups, Geometry, and Dynamics
Band
17
Ausgabe
1
Seite(n)
331-384
ISSN
1661-7207
eISSN
1661-7215
Page URI
https://pub.uni-bielefeld.de/record/2980275

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Petschick JM, Rajeev K. On the Basilica operation. Groups, Geometry, and Dynamics. 2023;17(1):331-384.
Petschick, J. M., & Rajeev, K. (2023). On the Basilica operation. Groups, Geometry, and Dynamics, 17(1), 331-384. https://doi.org/10.4171/GGD/702
Petschick, Jan Moritz, and Rajeev, Karthika. 2023. “On the Basilica operation”. Groups, Geometry, and Dynamics 17 (1): 331-384.
Petschick, J. M., and Rajeev, K. (2023). On the Basilica operation. Groups, Geometry, and Dynamics 17, 331-384.
Petschick, J.M., & Rajeev, K., 2023. On the Basilica operation. Groups, Geometry, and Dynamics, 17(1), p 331-384.
J.M. Petschick and K. Rajeev, “On the Basilica operation”, Groups, Geometry, and Dynamics, vol. 17, 2023, pp. 331-384.
Petschick, J.M., Rajeev, K.: On the Basilica operation. Groups, Geometry, and Dynamics. 17, 331-384 (2023).
Petschick, Jan Moritz, and Rajeev, Karthika. “On the Basilica operation”. Groups, Geometry, and Dynamics 17.1 (2023): 331-384.
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