Bulletin of Symbolic Logic 14 (4):449-480 (2008)

Abstract
This is an introductory survey of the emerging theory of two new classes of (discrete, countable) groups, called hyperlinear and sofic groups. They can be characterized as subgroups of metric ultraproducts of families of, respectively, unitary groups U (n) and symmetric groups $S_{n},\ n\in {\Bbb N}$ . Hyperlinear groups come from theory of operator algebras (Connes' Embedding Problem), while sofic groups, introduced by Gromov, are motivated by a problem of symbolic dynamics (Gottschalk's Surjunctivity Conjecture). Open questions are numerous, in particular it is still unknown if every group is hyperlinear and/or sofic
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DOI 10.2178/bsl/1231081461
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References found in this work BETA

[Omnibus Review].Akihiro Kanamori - 1981 - Journal of Symbolic Logic 46 (4):864-866.
Axioms of Symmetry: Throwing Darts at the Real Number Line.Chris Freiling - 1986 - Journal of Symbolic Logic 51 (1):190-200.

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Citations of this work BETA

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