A quasi-isometric embedding theorem for groups.

DOI10.1215/00127094-2266251zbMath1331.20054arXiv1202.6437OpenAlexW2141583892MaRDI QIDQ354036

Denis V. Osin, Alexander Yu. Ol'shanskii

Publication date: 17 July 2013

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1202.6437

zbMATH Keywords

finitely generated groupsHNN extensionssolvable groupsgroups of exponential growthamenable groupsleft invariant metricsbi-Lipschitz embeddingsFølner functionslength functions on groups

Mathematics Subject Classification ID

Subgroup theorems; subgroup growth (20E07) Solvable groups, supersolvable groups (20F16) Generators, relations, and presentations of groups (20F05) Geometric group theory (20F65) Extensions, wreath products, and other compositions of groups (20E22) Asymptotic properties of groups (20F69) Means on groups, semigroups, etc.; amenable groups (43A07)

Related Items (13)

Algebras and semigroups of locally subexponential growth ⋮ Følner functions and the generic word problem for finitely generated amenable groups ⋮ An introduction to the Ribe program ⋮ Computability of Følner sets ⋮ Distortion of imbeddings of groups of intermediate growth into metric spaces ⋮ Speed of random walks, isoperimetry and compression of finitely generated groups ⋮ Complexity among the finitely generated subgroups of Thompson's group ⋮ On matrix wreath products of algebras ⋮ Isoperimetric inequalities, shapes of Følner sets and groups with Shalom's property \(H_{\mathrm{FD}}\) ⋮ Matrix wreath products of algebras and embedding theorems ⋮ Group approximation in Cayley topology and coarse geometry Part I: Coarse embeddings of amenable groups ⋮ Elementary totally disconnected locally compact groups ⋮ Relative subgroup growth and subgroup distortion

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