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

Autor:	Jaikin-Zapirain, Andrei
Rok vydání:	2022
Předmět:	Mathematics - Group Theory Mathematics - Rings and Algebras
Druh dokumentu:	Working Paper
Popis:	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. Comment: Referee comments are included. It is also shown that the Q-completion of a limit group is residually torsion-free nilpotent. Accepted to Annales scientifiques de l'\'Ecole normale sup\'erieure
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2212.00402 Zobrazit plný text záznamu View this record from Arxiv