Grigorchuk-Erschler群的Basilica群
The Basilica group of the Grigorchuk-Erschler group
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中文总结 AI 辅助
本文利用Petschick和Rajeev构造的Basilica运算，证明Grigorchuk-Erschler群的第二个Basilica群存在无限指数的极大子群，丰富了有限生成分支群的相关研究。
中文摘要 AI 辅助
Francoeur和Garrido近期给出了有限生成分支群的首批明确例子，这类群包含无限指数的极大子群，其中一例为Grigorchuk-Erschler群。本文利用Petschick与Rajeev构造的Basilica运算，证明Grigorchuk-Erschler群的第二个Basilica群同样具有无限指数的极大子群。
英文摘要
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.
