On maximal subgroups of Thompson’s group

  • Gili Golan Polak

    Ben Gurion University of the Negev, Be’er Sheva, Israel
On maximal subgroups of Thompson’s group $F$ cover

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Abstract

We study subgroups of Thompson’s group by means of an automaton associated with them. We prove that every maximal subgroup of of infinite index is closed, that is, it coincides with the subgroup of accepted by the automaton associated with it. It follows that every finitely generated maximal subgroup of is undistorted in . We also prove that every finitely generated subgroup of is contained in a finitely generated maximal subgroup of and construct an infinite family of non-isomorphic maximal subgroups of infinite index in .

Cite this article

Gili Golan Polak, On maximal subgroups of Thompson’s group . Groups Geom. Dyn. (2024), published online first

DOI 10.4171/GGD/795