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Uniform Local Amenability implies Property A

Research output: Contribution to Journal/Magazine › Journal article › peer-review

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Uniform Local Amenability implies Property A. / Elek, Gabor.
In: Proceedings of the American Mathematical Society, Vol. 149, 18.03.2021, p. 2573-2577.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Elek, G 2021, 'Uniform Local Amenability implies Property A', Proceedings of the American Mathematical Society, vol. 149, pp. 2573-2577. https://doi.org/10.1090/proc/15387

APA

Elek, G. (2021). Uniform Local Amenability implies Property A. Proceedings of the American Mathematical Society, 149, 2573-2577. https://doi.org/10.1090/proc/15387

Vancouver

Elek G. Uniform Local Amenability implies Property A. Proceedings of the American Mathematical Society. 2021 Mar 18;149:2573-2577. Epub 2021 Mar 18. doi: 10.1090/proc/15387

Author

Elek, Gabor. / Uniform Local Amenability implies Property A. In: Proceedings of the American Mathematical Society. 2021 ; Vol. 149. pp. 2573-2577.

Bibtex

@article{027288e27d4240caac4f1aa05ba89e78,
title = "Uniform Local Amenability implies Property A",
abstract = "In this short note we answer a query of Brodzki, Niblo, \v{S}pakula, Willett and Wright \cite{ULA} by showing thatall bounded degree uniformly locally amenable graphs have Property A. For the second result of the noterecall that Kaiser \cite{Kaiser} proved that if $\Gamma$ is a finitely generated group and $\{H_i\}^\infty_{i=1}$ isa Farber sequence of finite index subgroups, then the associated Schreier graph sequence is of Property A if and only if the group is amenable.We show however, that there exist a non-amenable group and a nested sequence of finite index subgroups $\{H_i\}^\infty_{i=1}$ such that$\cap H_i=\{e_\Gamma\}$, and the associated Schreier graph sequence is of Property A.",
author = "Gabor Elek",
year = "2021",
month = mar,
day = "18",
doi = "10.1090/proc/15387",
language = "English",
volume = "149",
pages = "2573--2577",
journal = "Proceedings of the American Mathematical Society",
issn = "0002-9939",
publisher = "American Mathematical Society",

}

RIS

TY - JOUR

T1 - Uniform Local Amenability implies Property A

AU - Elek, Gabor

PY - 2021/3/18

Y1 - 2021/3/18

N2 - In this short note we answer a query of Brodzki, Niblo, \v{S}pakula, Willett and Wright \cite{ULA} by showing thatall bounded degree uniformly locally amenable graphs have Property A. For the second result of the noterecall that Kaiser \cite{Kaiser} proved that if $\Gamma$ is a finitely generated group and $\{H_i\}^\infty_{i=1}$ isa Farber sequence of finite index subgroups, then the associated Schreier graph sequence is of Property A if and only if the group is amenable.We show however, that there exist a non-amenable group and a nested sequence of finite index subgroups $\{H_i\}^\infty_{i=1}$ such that$\cap H_i=\{e_\Gamma\}$, and the associated Schreier graph sequence is of Property A.

AB - In this short note we answer a query of Brodzki, Niblo, \v{S}pakula, Willett and Wright \cite{ULA} by showing thatall bounded degree uniformly locally amenable graphs have Property A. For the second result of the noterecall that Kaiser \cite{Kaiser} proved that if $\Gamma$ is a finitely generated group and $\{H_i\}^\infty_{i=1}$ isa Farber sequence of finite index subgroups, then the associated Schreier graph sequence is of Property A if and only if the group is amenable.We show however, that there exist a non-amenable group and a nested sequence of finite index subgroups $\{H_i\}^\infty_{i=1}$ such that$\cap H_i=\{e_\Gamma\}$, and the associated Schreier graph sequence is of Property A.

U2 - 10.1090/proc/15387

DO - 10.1090/proc/15387

M3 - Journal article

VL - 149

SP - 2573

EP - 2577

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

ER -