Author

Gili Golan

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Preprint Sep 2026

Finiteness properties of closed subgroups of Thompson's group $F$

A subgroup $H$ of Thompson's group $F$ is closed if every piecewise-$H$ function in $F$ belongs to $H$. Prominent examples of closed subgroups are the maximal subgroups of infinite index, stabilizers and pointwise stabilizers of sets of points, and many of Jones'subgroups. A closed subgroup is finitely generated if and...

Gili Golan · 0 citations

Preprint Jul 2026

Higman--Thompson groups $F_n$ all the way down

We prove that for every $n\ge 2$ the Higman--Thompson group $F_n$ has a maximal subgroup of infinite index isomorphic to itself. In fact, we construct a chain of subgroups $F_n=H_0>H_1>H_2>\cdots$, all isomorphic to $F_n$ and with trivial intersection, such that for every $i$ the only subgroups of $F_n$ containing $H_i...

Gili Golan · 1 citation