Free $\mathbb Q$-groups are residually torsion-free nilpotent
Group Theory
2026-02-05 v3 Rings and Algebras
Abstract
We develop a method to show that some (abstract) groups can be embedded into a free pro- group. In particular, we show that a finitely generated subgroup of a free -group can be embedded into a free pro- group for almost all primes . This solves an old problem raised by G. Baumslag: free -groups are residually torsion-free nilpotent.
Keywords
Cite
@article{arxiv.2212.00402,
title = {Free $\mathbb Q$-groups are residually torsion-free nilpotent},
author = {Andrei Jaikin-Zapirain},
journal= {arXiv preprint arXiv:2212.00402},
year = {2026}
}
Comments
A mistake in the proof of Theorem 5.8 is corrected