Some remarks on Grothendieck pairs

Andrei Jaikin-Zapirain; Alexander Lubotzky

doi:10.4171/GGD/889

Some remarks on Grothendieck pairs

Andrei Jaikin-Zapirain
, Alexander Lubotzky

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Pages (from-to)	597-616
Number of pages	20
Journal	Groups, Geometry, and Dynamics
Volume	19
Issue number	2
DOIs	https://doi.org/10.4171/GGD/889
State	Published - 2025
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2025 European Mathematical Society.

Keywords

Grothendieck pairs
profinite rigidity

Access to Document

10.4171/GGD/889

Cite this

@article{12763d41e59f45c3b1b67e19f94846e1,

title = "Some remarks on Grothendieck pairs",

abstract = "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.",

keywords = "Grothendieck pairs, profinite rigidity",

author = "Andrei Jaikin-Zapirain and Alexander Lubotzky",

note = "Publisher Copyright: {\textcopyright} 2025 European Mathematical Society.",

year = "2025",

doi = "10.4171/GGD/889",

language = "אנגלית",

volume = "19",

pages = "597--616",

journal = "Groups, Geometry, and Dynamics",

issn = "1661-7207",

publisher = "European Mathematical Society Publishing House",

number = "2",

}

TY - JOUR

T1 - Some remarks on Grothendieck pairs

AU - Jaikin-Zapirain, Andrei

AU - Lubotzky, Alexander

PY - 2025

Y1 - 2025

N2 - 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.

AB - 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.

KW - Grothendieck pairs

KW - profinite rigidity

UR - https://www.scopus.com/pages/publications/105012853129

U2 - 10.4171/GGD/889

DO - 10.4171/GGD/889

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:105012853129

SN - 1661-7207

VL - 19

SP - 597

EP - 616

JO - Groups, Geometry, and Dynamics

JF - Groups, Geometry, and Dynamics

IS - 2

ER -

Some remarks on Grothendieck pairs

Abstract

Bibliographical note

Keywords

Access to Document

Other files and links

Fingerprint

Cite this