We demonstrate the existence of a family of finitely generated subgroups of Richard Thompson's group which is strictly well-ordered by the embeddability relation of type . All except the maximum element of this family (which is itself) are elementary amenable groups. In fact we also obtain, for each , a finitely generated elementary amenable subgroup of whose EA-class is . These groups all have simple, explicit descriptions and can be viewed as a natural continuation of the progression which starts with , , and the Brin–Navas group . We also give an example of a pair of finitely generated elementary amenable subgroups of with the property that neither is embeddable into the other.
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Collin Bleak, Matthew G. Brin, Justin Tatch Moore, Complexity among the finitely generated subgroups of Thompson's group. J. Comb. Algebra 5 (2021), no. 1, pp. 1–58DOI 10.4171/JCA/49