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arXiv · 2607.29449

The Basilica group of the Grigorchuk-Erschler group

Karthika Rajeev·Anitha Thillaisundaram
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Abstract

Francoeur and Garrido recently provided the first explicit examples of finitely generated branch groups with maximal subgroups of infinite index, where one of their examples is the Grigorchuk-Erschler group. Here, using the Basilica operation constructed by Petschick and Rajeev, we show that the second Basilica group of the Grigorchuk-Erschler group also has maximal subgroups of infinite index.

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Karthika Rajeev, Anitha Thillaisundaram. 2026-07-31. The Basilica group of the Grigorchuk-Erschler group. https://arxiv.org/abs/2607.29449

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