publication . Preprint . 2015

Uncountably many non-commensurable finitely presented pro-$p$ groups

Snopce, Ilir;
Open Access English
  • Published: 31 Mar 2015
Abstract
Let $m\geq 3$ be a positive integer. We prove that there are uncountably many non-commensurable metabelian uniform pro-$p$ groups of dimension $m$. Consequently, there are uncountably many non-commensurable finitely presented pro-$p$ groups with minimal number of generators $m$ (and minimal number of relations $ {m \choose 2}$).
Subjects
arXiv: Mathematics::Metric GeometryMathematics::Group Theory
free text keywords: Mathematics - Group Theory, 20E18, 22E20
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Universidade Federal do Rio de Janeiro, Instituto de Matema´tica, 21941-909 Rio de Janeiro, RJ, Brasil E-mail address: ilir@im.ufrj.br

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