Abstract
We demonstrate the existence of a family of finitely generated subgroups of Richard Thompson’s group F which is strictly wellordered by the embeddability relation of type ε_{0} + 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 < ε_{0}, a finitely generated elementary amenable subgroup of F whose EAclass 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 BrinNavas 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 language  English 

Pages (fromto)  158 
Number of pages  58 
Journal  Journal of Combinatorial Algebra 
Volume  5 
Issue number  1 
Early online date  7 Apr 2021 
DOIs  
Publication status  Published  2021 
Keywords
 Elementary amenable
 Elementary group
 Geometrically fast
 Homeomorphism group
 Ordinal
 Pean arithmetic
 Piecewise linear
 Thompson's group
 Transition chain
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Collin Patrick Bleak
 School of Mathematics and Statistics  Director of Impact
 Pure Mathematics  Reader
 Centre for Interdisciplinary Research in Computational Algebra
Person: Academic