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.
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This research was supported by Fundación La Caixa, Spain. I would like to thank my supervisor Prof. John S. Wilson for his help in the preparation of this paper and the referee for useful comments.
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Garrido, A. On the congruence subgroup problem for branch groups. Isr. J. Math. 216, 1–13 (2016). https://doi.org/10.1007/s11856-016-1402-x
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DOI: https://doi.org/10.1007/s11856-016-1402-x