2015arXiv (Cornell University)Open access

On hereditarily just infinite profinite groups obtained via iterated\n wreath products

Matteo Vannacci

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Abstract

We study a generalisation of the family of non-(virtually pro-$p$)\nhereditarily just infinite profinite groups introduced by J.\\! S.\\! Wilson in\n2010. We prove that this family contains groups of finite lower rank. We also\nshow that many groups in this family are not topologically finitely\npresentable.\n

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We study a generalisation of the family of non-(virtually pro-$p$)\nhereditarily just infinite profinite groups introduced by J.\\! S.\\! Wilson in\n2010. We prove that this family contains groups of finite lower rank. We also\nshow that many groups in this family are not topologically finitely\npresentable.\n

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We study a generalisation of the family of non-(virtually pro-$p$)\nhereditarily just infinite profinite groups introduced by J.\\! S.\\! Wilson in\n2010. We prove that this family contains groups of finite lower rank. We also\nshow that many groups in this family are not topologically finitely\npresentable.\n

Key concepts: Profinite group, Mathematics, Iterated function, Finitely-generated abelian group, Rank (graph theory), Pure mathematics, Wreath product, Combinatorics

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