Geodesic
On maximal subgroups of Thompson’s group $F$
Gili Golan Polak1 orcid
1Ben Gurion University of the Negev, Be’er Sheva, Israel
Groups, geometry, and dynamics, Tome 19 (2025) no. 3, pp. 797-860

Voir la notice de l'article provenant de la source EMS Press

DOI

We study subgroups of Thompson’s group F by means of an automaton associated with them. We prove that every maximal subgroup of F of infinite index is closed, that is, it coincides with the subgroup of F accepted by the automaton associated with it. It follows that every finitely generated maximal subgroup of F is undistorted in F. We also prove that every finitely generated subgroup of F is contained in a finitely generated maximal subgroup of F and construct an infinite family of non-isomorphic maximal subgroups of infinite index in F.
DOI : 10.4171/ggd/795
Classification : 20F65, 20E28, 20F10
Mots-clés : Thompson’s group F, maximal subgroups, closed subgroups

Gili Golan Polak  1

1 Ben Gurion University of the Negev, Be’er Sheva, Israel 
Gili Golan Polak. On maximal subgroups of Thompson’s group $F$. Groups, geometry, and dynamics, Tome 19 (2025) no. 3, pp. 797-860. doi: 10.4171/ggd/795
@article{10_4171_ggd_795,
     author = {Gili Golan Polak},
     title = {On maximal subgroups of {Thompson{\textquoteright}s} group $F$},
     journal = {Groups, geometry, and dynamics},
     pages = {797--860},
     year = {2025},
     volume = {19},
     number = {3},
     doi = {10.4171/ggd/795},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/795/}
}
TY  - JOUR
AU  - Gili Golan Polak
TI  - On maximal subgroups of Thompson’s group $F$
JO  - Groups, geometry, and dynamics
PY  - 2025
SP  - 797
EP  - 860
VL  - 19
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4171/ggd/795/
DO  - 10.4171/ggd/795
ID  - 10_4171_ggd_795
ER  - 
%0 Journal Article
%A Gili Golan Polak
%T On maximal subgroups of Thompson’s group $F$
%J Groups, geometry, and dynamics
%D 2025
%P 797-860
%V 19
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4171/ggd/795/
%R 10.4171/ggd/795
%F 10_4171_ggd_795

Cité par Sources :