On sofic groups

By Gábor Elek, Endre Szabó. 2003

112 citations recorded by the source corpus.

Abstract Answering some questions of Weiss in [B. Weiss. Sofic groups and dynamical systems. (Ergodic theory and harmonic analysis, Mumbai, 1999.) Sankhya Ser. A. 62 (2000), 350-359.], we prove that a free product of sofic groups is sofic and that amenable extensions of sofic groups are sofic. We also give an example of a finitely generated sofic group that is not residually amenable.

Subfields: Control and Systems Engineering, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/9ef580b376f5ca1378b356f5402657a120c831c4

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Control and Systems Engineering

1. W. Lück
2. Arthur Bartels
3. Tullio Ceccherini-Silberstein
4. Michel Coornaert
5. Gábor Elek
6. Endre Szabó

In Geometry and Topology

1. W. Lück
2. Arthur Bartels
3. H. Reich
4. Michel Coornaert
5. Tullio Ceccherini-Silberstein
6. Gábor Elek
7. Valerio Capraro
8. Martino Lupini

In Mathematical Physics

1. W. Lück
2. Arthur Bartels
3. H. Reich
4. Valerio Capraro
5. Martino Lupini
6. Michel Coornaert
7. Tullio Ceccherini-Silberstein
8. Gábor Elek

Citations in the corpus

• On the Farrell–Jones Conjecture and its applications (2007, background): “For more information about the notion of a sofic group, we refer to [26].”
• The K-theoretic Farrell–Jones conjecture for hyperbolic groups (2007, background): “(For the notion of a sofic group we refer for instance to [21].”
• Injective linear cellular automata and sofic groups (2007, background): “The class of sofic groups contains, in particular, all residually amenable groups and it is closed under direct products, free products, taking subgroups and extensions by amenable groups [ ES2 ].”
• Introduction to Sofic and Hyperlinear Groups and Connes' Embedding Conjecture (2013, background): “The fact that a free product of sofic groups is sofic has been first proven in [39].”
• Hyperlinearity, essentially free actions and L2-invariants. The sofic property (2004, background): “Residually amenable groups are sofic, however there exist finitely generated non-residually amenable sofic groups as well [ 6 ].”
• Sofic equivalence relations (2009, background): “Residually amenable groups are sofic, however there exist finitely generated non-residually amenable sofic groups as well [5].”