Uncountably many non-commensurable finitely presented pro-p groups

  title={Uncountably many non-commensurable finitely presented pro-p groups},
  author={Ilir Snopce},
  journal={Journal of Group Theory},
  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${ \binom{m}{2}}$ ). 
Uncountably many non-commensurable pro-p groups of homological type FPk but not FPk+1
  • D. Kochloukova
  • 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.
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-injectiveExpand
On hereditarily self-similar $p$-adic analytic pro-$p$ groups
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 faithfulExpand
On pro-$p$ groups with quadratic cohomology
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 maximalExpand


Normal Zeta Functions of Some pro-p Groups
We give an explicit formula for the number of normal subgroups of index p n of the pro-p group , and for the normal zeta function associated with this group. Let 𝒬1(s, r) be the subgroups of theExpand
Powerful p-groups. II. p-adic analytic groups
We apply our results from the first part [LM] to p-adic analytic pro-p groups, i.e., pro-p groups which are Lie groups over the field of p-adic numbers. For a systematic study of these groups seeExpand
Groupes analytiques p-adiques
© Association des collaborateurs de Nicolas Bourbaki, 1964, tous droits réservés. L’accès aux archives du séminaire Bourbaki (http://www.bourbaki. ens.fr/) implique l’accord avec les conditionsExpand
Analytic Pro-p Groups, 2nd ed
  • Cambridge Stud. Adv. Math
  • 1999
Powerful p-groups
  • II. p-adic analytic groups, J. Algebra 105
  • 1987
Finiteness Conditions for Soluble Groups