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

Ilir Snopce

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

Group Theory 2015-04-02 v1

Authors: Ilir Snopce

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 ${m \choose 2}$ ).

Keywords

finite groups combinatorial group theory group theory

Cite

@article{arxiv.1504.00027,
  title  = {Uncountably many non-commensurable finitely presented pro-$p$ groups},
  author = {Ilir Snopce},
  journal= {arXiv preprint arXiv:1504.00027},
  year   = {2015}
}

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