1Universidad Complutense de Madrid, Spain; CSIC-UAM-UC3M-UCM, Madrid, Spain 2Hofstra University, Hempstead, USA; Ss. Cyril and Methodius University in Skopje, North Macedonia
Groups, geometry, and dynamics, Tome 19 (2025) no. 2, pp. 567-596
A theoretical framework is established for explicitly calculating rigid kernels of self-similar regular branch groups. This is applied to a new infinite family of branch groups in order to provide the first examples of self-similar, branch groups with infinite rigid kernel. The groups are analogues of the Hanoi Towers group on 3 pegs, based on the standard actions of finite dihedral groups on regular polygons with odd numbers of vertices, and the rigid kernel is an infinite Cartesian power of the cyclic group of order 2, except for the original Hanoi group. The proofs rely on a symbolic-dynamical approach, related to finitely constrained groups.
1
Universidad Complutense de Madrid, Spain; CSIC-UAM-UC3M-UCM, Madrid, Spain
2
Hofstra University, Hempstead, USA; Ss. Cyril and Methodius University in Skopje, North Macedonia
Alejandra Garrido; Zoran Šunić. Branch groups with infinite rigid kernel. Groups, geometry, and dynamics, Tome 19 (2025) no. 2, pp. 567-596. doi: 10.4171/ggd/888
@article{10_4171_ggd_888,
author = {Alejandra Garrido and Zoran \v{S}uni\'c},
title = {Branch groups with infinite rigid kernel},
journal = {Groups, geometry, and dynamics},
pages = {567--596},
year = {2025},
volume = {19},
number = {2},
doi = {10.4171/ggd/888},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/888/}
}
TY - JOUR
AU - Alejandra Garrido
AU - Zoran Šunić
TI - Branch groups with infinite rigid kernel
JO - Groups, geometry, and dynamics
PY - 2025
SP - 567
EP - 596
VL - 19
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.4171/ggd/888/
DO - 10.4171/ggd/888
ID - 10_4171_ggd_888
ER -
