Metric properties of Diestel-Leader groups.

DOI10.1307/mmj/1370870377zbMath1288.20054arXiv1202.4199OpenAlexW2963534822MaRDI QIDQ357526

Jennifer Taback, Melanie Stein

Publication date: 30 July 2013

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

Full work available at URL: https://arxiv.org/abs/1202.4199

zbMATH Keywords

finitely generated groupsCayley graphsgenerating setsfinitely presented groupsword lengthsautomata groupsself-similar groupsdead-end elementsDiestel-Leader graphsDiestel-Leader groupslamplighter groupsproducts of trees

Mathematics Subject Classification ID

Trees (05C05) Generators, relations, and presentations of groups (20F05) Geometric group theory (20F65) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Extensions, wreath products, and other compositions of groups (20E22)

Related Items

On the asymmetry of stars at infinity, Higher rank lamplighter groups are graph automatic, Geometry of the conjugacy problem in lamplighter groups, On the bi-Lipschitz geometry of lamplighter graphs, A characterization of superreflexivity through embeddings of lamplighter groups

Cites Work

• Unnamed Item
• Unnamed Item
• The Dehn function of Baumslag's metabelian group.
• Coarse differentiation of quasi-isometries. I: Spaces not quasi-isometric to Cayley graphs
• Metabelian groups with quadratic Dehn function and Baumslag-Solitar groups.
• Spectral computations on lamplighter groups and Diestel-Leader graphs
• Horocyclic products of trees
• The combinatorial structure of cocompact discrete hyperbolic groups
• The geometry of twisted conjugacy classes in wreath products
• THE UNBOUNDED DEAD-END DEPTH PROPERTY IS NOT A GROUP INVARIANT
• Erratum to ``A finitely presented group with unbounded dead-end depth
• Lamplighters, Diestel–Leader Graphs, Random Walks, and Harmonic Functions
• A finitely presented group with unbounded dead-end depth
• A conjecture concerning a limit of non-Cayley graphs