Some remarks on Grothendieck pairs

2024/01/04 by Jaikin-Zapirain, Andrei, Lubotzky, Alexander
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2401.02229

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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