Embeddings into Thompson's group V and coCF groups
Date
10/2016Metadata
Show full item recordAbstract
It is shown in Lehnert and Schweitzer (‘The co-word problem for the Higman–Thompson group is context-free’, Bull. London Math. Soc. 39 (2007) 235–241) that R. Thompson's group V is a cocontext-context-free (coCF) group, thus implying that all of its finitely generated subgroups are also coCF groups. Also, Lehnert shows in his thesis that V embeds inside the coCF group QAut(T2,c), which is a group of particular bijections on the vertices of an infinite binary 2-edge-coloured tree, and he conjectures that QAut(T2,c) is a universal coCF group. We show that QAut(T2,c) embeds into V, and thus obtain a new form for Lehnert's conjecture. Following up on these ideas, we begin work to build a representation theory into R. Thompson's group V. In particular, we classify precisely which Baumslag–Solitar groups embed into V.
Citation
Bleak , C , Matucci , F & Neunhöffer , M 2016 , ' Embeddings into Thompson's group V and coCF groups ' , Journal of the London Mathematical Society , vol. 94 , no. 2 , pp. 583-597 . https://doi.org/10.1112/jlms/jdw044
Publication
Journal of the London Mathematical Society
Status
Peer reviewed
ISSN
0024-6107Type
Journal article
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