Uncountably many non-commensurable finitely presented pro-p groups

@article{Snopce2015UncountablyMN,
  title={Uncountably many non-commensurable finitely presented pro-p groups},
  author={Ilir Snopce},
  journal={Journal of Group Theory},
  year={2015},
  volume={19},
  pages={515 - 521}
}
  • I. Snopce
  • Published 31 March 2015
  • Mathematics
  • Journal of Group Theory
Abstract Let m ≥ 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 2${ \binom{m}{2}}$ ). 
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