Abstract
It is shown in Lehnert and Schweitzer (‘The coword problem for the Higman–Thompson group is contextfree’, Bull. London Math. Soc. 39 (2007) 235–241) that R. Thompson's group V is a cocontextcontextfree (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(T_{2,c}), which is a group of particular bijections on the vertices of an infinite binary 2edgecoloured tree, and he conjectures that QAut(T_{2,c}) is a universal coCF group. We show that QAut(T_{2,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.
Original language  English 

Pages (fromto)  583597 
Number of pages  15 
Journal  Journal of the London Mathematical Society 
Volume  94 
Issue number  2 
Early online date  25 Jul 2016 
DOIs  
Publication status  Published  Oct 2016 
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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