Uncountably many non-commensurable finitely presented pro-p groups
classification
🧮 math.GR
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groupsmanynon-commensurablepro-uncountablyfinitelyminimalnumber
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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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