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dc.contributor.authorBleak, Collin
dc.contributor.authorBrin, Matthew G.
dc.contributor.authorMoore, Justin Tatch
dc.date.accessioned2021-03-02T13:30:01Z
dc.date.available2021-03-02T13:30:01Z
dc.date.issued2021
dc.identifier251767120
dc.identifier15ebaae2-acd5-4655-9fc7-6e2d63f55b70
dc.identifier000638255700001
dc.identifier85105535942
dc.identifier.citationBleak , 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/49en
dc.identifier.issn2415-6302
dc.identifier.otherArXiv: http://arxiv.org/abs/1711.10998v1
dc.identifier.otherORCID: /0000-0001-5790-1940/work/92371880
dc.identifier.urihttps://hdl.handle.net/10023/21538
dc.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.en
dc.description.abstractWe 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.
dc.format.extent58
dc.format.extent486587
dc.language.isoeng
dc.relation.ispartofJournal of Combinatorial Algebraen
dc.subjectElementary amenableen
dc.subjectElementary groupen
dc.subjectGeometrically fasten
dc.subjectHomeomorphism groupen
dc.subjectOrdinalen
dc.subjectPean arithmeticen
dc.subjectPiecewise linearen
dc.subjectThompson's groupen
dc.subjectTransition chainen
dc.subjectQA Mathematicsen
dc.subjectAlgebra and Number Theoryen
dc.subjectDiscrete Mathematics and Combinatoricsen
dc.subjectT-NDASen
dc.subjectBDUen
dc.subject.lccQAen
dc.titleComplexity among the finitely generated subgroups of Thompson's groupen
dc.typeJournal articleen
dc.contributor.institutionUniversity of St Andrews. School of Mathematics and Statisticsen
dc.contributor.institutionUniversity of St Andrews. Pure Mathematicsen
dc.contributor.institutionUniversity of St Andrews. Centre for Interdisciplinary Research in Computational Algebraen
dc.identifier.doi10.4171/JCA/49
dc.description.statusPeer revieweden
dc.identifier.urlhttps://arxiv.org/abs/1711.10998en


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