2015arXiv (Cornell University)Open access

On hereditarily just infinite profinite groups obtained via iterated wreath products

Matteo Vannacci

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Abstract

We study a generalisation of the family of non-(virtually pro-$p$) hereditarily just infinite profinite groups introduced by J.\! S.\! Wilson in 2010. We prove that this family contains groups of finite lower rank. We also show that many groups in this family are not topologically finitely presentable.

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We study a generalisation of the family of non-(virtually pro-$p$) hereditarily just infinite profinite groups introduced by J.\! S.\! Wilson in 2010. We prove that this family contains groups of finite lower rank. We also show that many groups in this family are not topologically finitely presentable.

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Available abstract

We study a generalisation of the family of non-(virtually pro-$p$) hereditarily just infinite profinite groups introduced by J.\! S.\! Wilson in 2010. We prove that this family contains groups of finite lower rank. We also show that many groups in this family are not topologically finitely presentable.

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

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