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- W2953126783 abstract "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 (also known as V) 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 plynomial time). We show that the generalized word problem of T_fin is undecidable. We study the distortion functions of T_fin and we show that T_fin contains all finite direct products of finitely generated free groups as subgroups with linear distortion. As a consequence, up to polynomial equivalence of functions, the following three sets are the same: the set of distortions of T_fin, the set of all Dehn functions of finitely presented groups, and the set of time complexity functions of nondeterministic Turing machines." @default.
- W2953126783 created "2019-06-27" @default.
- W2953126783 creator A5065749291 @default.
- W2953126783 date "2002-04-24" @default.
- W2953126783 modified "2023-09-23" @default.
- W2953126783 title "The groups of Richard Thompson and complexity" @default.
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- W2953126783 hasPublicationYear "2002" @default.
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