Some remarks on Grothendieck pairs
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866914304546045952 |
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| author | Jaikin-Zapirain, Andrei Lubotzky, Alexander |
| author_facet | Jaikin-Zapirain, Andrei Lubotzky, Alexander |
| contents | We revisit the paper of Alexander Grothendiek where he introduced Grothendieck pairs and discuss the relation between profinite rigidity and left/right Grothendieck rigidity. We also show that various groups are left and/or right Grothendieck rigid and, in particular, all ascending HNN extensiona of finitely generated free groups are right Grothendieck rigid. Along the way we present a number of questions and suggestions for further research. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_02229 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Some remarks on Grothendieck pairs Jaikin-Zapirain, Andrei Lubotzky, Alexander Group Theory We revisit the paper of Alexander Grothendiek where he introduced Grothendieck pairs and discuss the relation between profinite rigidity and left/right Grothendieck rigidity. We also show that various groups are left and/or right Grothendieck rigid and, in particular, all ascending HNN extensiona of finitely generated free groups are right Grothendieck rigid. Along the way we present a number of questions and suggestions for further research. |
| title | Some remarks on Grothendieck pairs |
| topic | Group Theory |
| url | https://arxiv.org/abs/2401.02229 |