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arXiv · 2212.00402

Free $\mathbb Q$-groups are residually torsion-free nilpotent

Andrei Jaikin-Zapirain
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Abstract

We develop a method to show that some (abstract) groups can be embedded into a free pro-$p$ group. In particular, we show that a finitely generated subgroup of a free $\mathbb Q$-group can be embedded into a free pro-$p$ group for almost all primes $p$. This solves an old problem raised by G. Baumslag: free $\mathbb Q$-groups are residually torsion-free nilpotent.

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Andrei Jaikin-Zapirain. 2022-12-01. Free $\mathbb Q$-groups are residually torsion-free nilpotent. https://arxiv.org/abs/2212.00402

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