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2021•arXiv (Cornell University)Open access

Torsion growth in finitely presented pro-$p$ groups

Nikolay M. Nikolov

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Abstract

We prove that torsion in the abelianizations of open normal subgroups in finitely presented pro-$p$ groups can grow arbitrarily fast. By way of contrast in $\mathbb Z_p$- analytic groups the torsion growth is at most polynomial.

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What this paper is about

We prove that torsion in the abelianizations of open normal subgroups in finitely presented pro-$p$ groups can grow arbitrarily fast. By way of contrast in $\mathbb Z_p$- analytic groups the torsion growth is at most polynomial.

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Available abstract

We prove that torsion in the abelianizations of open normal subgroups in finitely presented pro-$p$ groups can grow arbitrarily fast. By way of contrast in $\mathbb Z_p$- analytic groups the torsion growth is at most polynomial.

Key concepts: Torsion (gastropod), Finitely-generated abelian group, Mathematics, Pure mathematics, Combinatorics, Biology, Anatomy

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