The infinite simple group V of Richard J. Thompson : presentations by permutations
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We show that one can naturally describe elements of R. Thompson's finitely presented infinite simple group V, known by Thompson to have a presentation with four generators and fourteen relations, as products of permutations analogous to transpositions. This perspective provides an intuitive explanation towards the simplicity of V and also perhaps indicates a reason as to why it was one of the first discovered infinite finitely presented simple groups: it is (in some basic sense) a relative of the finite alternating groups. We find a natural infinite presentation for V as a group generated by these "transpositions," which presentation bears comparison with Dehornoy's infinite presentation and which enables us to develop two small presentations for V: a human-interpretable presentation with three generators and eight relations, and a Tietze-derived presentation with two generators and seven relations.
Bleak , C & Quick , M 2017 , ' The infinite simple group V of Richard J. Thompson : presentations by permutations ' Groups, Geometry, and Dynamics , vol 11 , no. 4 , pp. 1401-1436 . DOI: 10.4171/GGD/433
Groups, Geometry, and Dynamics
© 2017, EMS Publishing House. This work has been 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 https://doi.org/10.4171/GGD/433
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