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arXiv · 1504.00027

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

Ilir Snopce
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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}$).

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Ilir Snopce. 2015-03-31. Uncountably many non-commensurable finitely presented pro-$p$ groups. https://arxiv.org/abs/1504.00027

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