Instability of the virtual solvability and the property of being virtually torsion-free for quasi-isometric groups

1999/11/14 by Anna Dioubina, Dioubina, Anna · 1 citation
Mathematics · #20F65 #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Mathematical Dynamics and Fractals #advanced mathematical theories #math.GR #msc:20F65

paper · pdf · doi:10.48550/arxiv.math/9911099

arxiv created 1999/11/14 · openalex publication_date 1999/11/14 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct examples of groups showing that virtual solvability and the property of being virtually torsion-free are not preserved by bi-Lipschitz maps and hence by quasi-isometries.

Cited by

• Rigidity and flexibility results for groups with a common cocompact envelope

Related

• Uncountably many quasi-isometric torsion-free groups
• Problems on the geometry of finitely generated solvable groups
• Quasi-isometry rigidity of groups
• A geometric obstruction to self-simulation for groups
• Quasi-isometries and rigidity of solvable groups