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December 2008 Hyperlinear and sofic groups: a brief guide
Vladimir G. Pestov
Bull. Symbolic Logic 14(4): 449-480 (December 2008). DOI: 10.2178/bsl/1231081461

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∈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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Vladimir G. Pestov. "Hyperlinear and sofic groups: a brief guide." Bull. Symbolic Logic 14 (4) 449 - 480, December 2008. https://doi.org/10.2178/bsl/1231081461

Information

Published: December 2008
First available in Project Euclid: 4 January 2009

zbMATH: 1206.20048
MathSciNet: MR2460675
Digital Object Identifier: 10.2178/bsl/1231081461

Subjects:
Primary: 03C20, 20F69, 37B10, 46L10

Rights: Copyright © 2008 Association for Symbolic Logic

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Vol.14 • No. 4 • December 2008
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