On the congruence subgroup problem for branch groups

Abstract

We answer a question of Bartholdi, Siegenthaler and Zalesskii, showing that the congruence subgroup problem for branch groups is independent of the branch action on a tree. We prove that the congruence topology of a branch group is determined by the group; specifically, by its structure graph, an object first introduced by Wilson. We also give a more natural definition of this graph.

9 pages, no figures; minor changes in accordance with referee report, exposition improved

Cited by in corpus (3)

• Locally normal subgroups of totally disconnected groups. Part II: Compactly generated simple groups
• Pro-$\mathcal{C}$ congruence properties for groups of rooted tree automorphisms
• On the congruence subgroup property for GGS-groups