The Basilica group of the Grigorchuk-Erschler group
arXiv:2607.29449
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.
16 pages