English

Some remarks on Grothendieck pairs

Group Theory 2026-02-05 v2

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.

Keywords

Cite

@article{arxiv.2401.02229,
  title  = {Some remarks on Grothendieck pairs},
  author = {Andrei Jaikin-Zapirain and Alexander Lubotzky},
  journal= {arXiv preprint arXiv:2401.02229},
  year   = {2026}
}

Comments

Published in Groups Geom. Dyn. 19 (2025), no. 2, 597-616