Complexity among the finitely generated subgroups of Thompson's group
Abstract
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.
Citation
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
Publication
Journal of Combinatorial Algebra
Status
Peer reviewed
DOI
10.4171/JCA/49ISSN
2415-6302Type
Journal article
Description
Funding: 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.Collections
Items in the St Andrews Research Repository are protected by copyright, with all rights reserved, unless otherwise indicated.