Complexity among the finitely generated subgroups of Thompson's group
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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.
Bleak , C , Brin , M G & Moore , J T 2021 , ' Complexity among the finitely generated subgroups of Thompson's group ' , Journal of Combinatorial Algebra , vol. 5 , no. 1 , pp. 1-58 . https://doi.org/10.4171/JCA/49
Journal of Combinatorial Algebra
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DescriptionFunding: Acknowledgements. The authors would also like to thank the referee for their very careful and thorough reading of the paper. This publication is in part a product of a visit of the first and third author to the Mathematisches Forschungsinstitut Oberwolfach, Germany in December 2016 as part of their Research In Pairs program. The third author was partially supported by NSF grants DMS–1600635 and DMS-1854367.
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