# 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} }

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${ \binom{m}{2}}$ ).

#### 4 Citations

Uncountably many non-commensurable pro-p groups of homological type FPk but not FPk+1

- Computer Science, Mathematics
- Int. J. Algebra Comput.
- 2019

We show that there are uncountably many non-commensurable metabelian pro-[Formula: see text] groups of homological type [Formula: see text] but not of type [Formula: see text], generated by [Formula:… Expand

Frattini-injectivity and Maximal pro-$p$ Galois groups.

- Mathematics
- 2020

We call a pro-$p$ group $G$ Frattini-injective if distinct finitely generated subgroups of $G$ have distinct Frattinis. This paper is an initial effort toward a systematic study of Frattini-injective… Expand

On hereditarily self-similar $p$-adic analytic pro-$p$ groups

- Mathematics
- 2020

A non-trivial finitely generated pro-$p$ group $G$ is said to be strongly hereditarily self-similar of index $p$ if every non-trivial finitely generated closed subgroup of $G$ admits a faithful… Expand

On pro-$p$ groups with quadratic cohomology

- Mathematics
- 2019

The main purpose of this article is to study pro-$p$ groups with quadratic $\mathbb{F}_p$-cohomology algebra, i.e. $H^\bullet$-quadratic pro-$p$ groups. Prime examples of such groups are the maximal… Expand

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