Embeddings into Thompson's group V and coCF groups
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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.
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
Journal of the London Mathematical Society
© 2016 London Mathematical Society. This work is made available online in accordance with the publisher’s policies. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at http://jlms.oxfordjournals.org/ https://dx.doi.org/10.1112/jlms/jdw044