We revisit the paper of Alexander Grothendieck 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-extensions of finitely generated free groups are right Grothendieck rigid. Along the way we present a number of questions and suggestions for further research.
1
Universidad Autónoma de Madrid, Spain; Instituto de Ciencias Matemáticas, Madrid, Spain
2
Weizmann Institute of Science, Rehovot, Israel
Andrei Jaikin-Zapirain; Alexander Lubotzky. Some remarks on Grothendieck pairs. Groups, geometry, and dynamics, Tome 19 (2025) no. 2, pp. 597-616. doi: 10.4171/ggd/889
@article{10_4171_ggd_889,
author = {Andrei Jaikin-Zapirain and Alexander Lubotzky},
title = {Some remarks on {Grothendieck} pairs},
journal = {Groups, geometry, and dynamics},
pages = {597--616},
year = {2025},
volume = {19},
number = {2},
doi = {10.4171/ggd/889},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/889/}
}
TY - JOUR
AU - Andrei Jaikin-Zapirain
AU - Alexander Lubotzky
TI - Some remarks on Grothendieck pairs
JO - Groups, geometry, and dynamics
PY - 2025
SP - 597
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VL - 19
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.4171/ggd/889/
DO - 10.4171/ggd/889
ID - 10_4171_ggd_889
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