Complexity among the finitely generated subgroups of Thompson's group

Collin Bleak, Matthew G. Brin, Justin Tatch Moore

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2 Citations (Scopus)
3 Downloads (Pure)


We demonstrate the existence of a family of finitely generated subgroups of Richard Thompson’s group F which is strictly well-ordered by the embeddability relation of type ε0 + 1. All except the maximum element of this family (which is F itself) are elementary amenable groups. In fact we also obtain, for each α < ε0, a finitely generated elementary amenable subgroup of F whose EA-class is α + 2. These groups all have simple, explicit descriptions and can be viewed as a natural continuation of the progression which starts with Z + Z, Z wr Z, and the Brin-Navas group B. We also give an example of a pair of finitely generated elementary amenable subgroups of F with the property that neither is embeddable into the other.
Original languageEnglish
Pages (from-to)1-58
Number of pages58
JournalJournal of Combinatorial Algebra
Issue number1
Early online date7 Apr 2021
Publication statusPublished - 2021


  • Elementary amenable
  • Elementary group
  • Geometrically fast
  • Homeomorphism group
  • Ordinal
  • Pean arithmetic
  • Piecewise linear
  • Thompson's group
  • Transition chain


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