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THE GROUPS OF RICHARD THOMPSON AND COMPLEXITY
2004
International journal of algebra and computation
We prove new results about the remarkable infinite simple groups introduced by Richard Thompson in the 1960s. We define the groups as partial transformation groups and we give a faithful representation in the Cuntz C ⋆ -algebra. For the finitely presented simple group T fin we show that the word-length and the table size satisfy an n log n relation, just like the symmetric groups. We show that the word problem of T fin belongs to the parallel complexity class AC 1 (a subclass of P). We show
doi:10.1142/s0218196704001980
fatcat:gsztws2lbfdobcldqh7ndu6wmq