Gábor Elek
Hungarian Academy of Sciences
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Publication
Featured researches published by Gábor Elek.
Journal of Group Theory | 2006
Gábor Elek; Endre Szabó
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.
arXiv: Combinatorics | 2010
Gábor Elek; Gabor Lippner
In 2008 Nguyen and Onak constructed the first constant-time algorithm for the approximation of the size of the maximum matching in bounded degree graphs. The Borel oracle machinery is a tool that can be used to convert some statements in Borel graph theory to theorems in the field of constant-time algorithms. In this paper we illustrate the power of this tool to prove the existence of the above mentioned constant-time approximation algorithm.
Bulletin of The London Mathematical Society | 2003
Gábor Elek
In this note we prove that in the case of finitely generated amenable groups the classical zero divisor conjecture implies the analytic zero divisor conjecture of Linnell.
arXiv: Group Theory | 2011
Gábor Elek; Endre Szabó
Using probabilistic methods, Collins and Dykema proved that the free product of two sofic groups amalgamated over a monotileably amenable subgroup is sofic as well. We show that the restriction is unnecessary; the free product of two sofic groups amalgamated over an arbitrary amenable subgroup is sofic. We also prove a group theoretical analogue of a result of Kenley Jung. A finitely generated group is amenable if and only if it has only one sofic representation up to conjugacy equivalence.
Combinatorica | 2010
Gábor Elek
Let d≥2 be given and let µ be an involution-invariant probability measure on the space of trees T ∈ Td with maximum degrees at most d. Then µ arises as the local limit of some sequence {Gn}n=1∞ of graphs with all degrees at most d. This answers Question 3.3 of Bollobás and Riordan [4].
Combinatorica | 2007
Gábor Elek
We prove that for any weakly convergent sequence of finite graphs with bounded vertex degrees, there exists a topological limit graphing.
Ergodic Theory and Dynamical Systems | 2012
Miklos Abert; Gábor Elek
We study profinite actions of residually finite groups in terms of weak containment. We show that two strongly ergodic profinite actions of a group are weakly equivalent if and only if they are isomorphic. This allows us to construct continuum many pairwise weakly inequivalent free actions of a large class of groups, including free groups and linear groups with property (T). We also prove that for chains of subgroups of finite index, Lubotzkys property (
Journal of Algebra | 2003
Gábor Elek
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Journal of Molecular Medicine | 1982
Gábor Elek; Antal Rockenbauer
) is inherited when taking the intersection with a fixed subgroup of finite index. That this is not true for families of subgroups in general leads to answering the question of Lubotzky and Zuk, whether for families of subgroups, property (
Proceedings of the American Mathematical Society | 2003
Gábor Elek
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