On Maximal Subgroups of Thompson's Group $F$
Gili Golan

TL;DR
This paper investigates the structure of maximal subgroups in Thompson's group F, showing they are closed, undistorted, and constructing many examples of such subgroups, advancing understanding of subgroup dynamics in F.
Contribution
It proves that all infinite index maximal subgroups of F are closed and constructs numerous non-isomorphic examples, providing new insights into subgroup structure.
Findings
Maximal subgroups of infinite index in F are closed.
Finitely generated subgroups are contained in finitely generated maximal subgroups.
Constructed an infinite family of non-isomorphic maximal subgroups of infinite index.
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 .
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Taxonomy
TopicsFinite Group Theory Research · Advanced Operator Algebra Research · Rings, Modules, and Algebras
