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.
Original language | English |
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Pages (from-to) | 1-58 |
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