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arXiv · 2401.02229

Some remarks on Grothendieck pairs

Andrei Jaikin-Zapirain·Alexander Lubotzky
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Abstract

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.

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Andrei Jaikin-Zapirain, Alexander Lubotzky. 2026-02-03. Some remarks on Grothendieck pairs. https://arxiv.org/abs/2401.02229

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