Duke Mathematical Journal

A quasi-isometric embedding theorem for groups

Alexander Yu. Olshanskii and Denis V. Osin

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We show that every group H of at most exponential growth with respect to some left invariant metric admits a bi-Lipschitz embedding into a finitely generated group G such that G is amenable (resp., solvable, satisfies a nontrivial identity, elementary amenable, of finite decomposition complexity) whenever H also shares those conditions. We also discuss some applications to compression functions of Lipschitz embeddings into uniformly convex Banach spaces, Følner functions, and elementary classes of amenable groups.

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Duke Math. J., Volume 162, Number 9 (2013), 1621-1648.

First available in Project Euclid: 11 June 2013

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Zentralblatt MATH identifier

Primary: 20F65: Geometric group theory [See also 05C25, 20E08, 57Mxx] 20F69: Asymptotic properties of groups
Secondary: 20F16: Solvable groups, supersolvable groups [See also 20D10] 20E22: Extensions, wreath products, and other compositions [See also 20J05]


Olshanskii, Alexander Yu.; Osin, Denis V. A quasi-isometric embedding theorem for groups. Duke Math. J. 162 (2013), no. 9, 1621--1648. doi:10.1215/00127094-2266251. https://projecteuclid.org/euclid.dmj/1370955541

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