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

2022/12/01 by Andrei Jaikin‐Zapirain, Jaikin-Zapirain, Andrei
Mathematics · #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR) #Rings and Algebras (math.RA) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2212.00402

openalex publication_date 2022/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

• Embeddings into pro-p groups and the construction of parafree groups
• Second Countable Virtually Free Pro-p Groups whose Torsion Elements have\n Finite Centralizer
• Addendum: Virtually Free pro-p groups whose Torsion Elements have finite Centralizer
• Profinite properties of residually free groups
• Generalizing Magnus' characterization of free groups to some free products