Free $\mathbb Q$-groups are residually torsion-free nilpotent
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866917245927555072 |
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| author | Jaikin-Zapirain, Andrei |
| author_facet | Jaikin-Zapirain, Andrei |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_00402 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Free $\mathbb Q$-groups are residually torsion-free nilpotent Jaikin-Zapirain, Andrei Group Theory Rings and Algebras 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. |
| title | Free $\mathbb Q$-groups are residually torsion-free nilpotent |
| topic | Group Theory Rings and Algebras |
| url | https://arxiv.org/abs/2212.00402 |