A note on approximate subgroups of GL_n(C) and uniformly nonamenable groups

2011/01/13 by Emmanuel Breuillard, Breuillard, Emmanuel, Ben Green +3
Mathematics · #Advanced Algebra and Geometry #Advanced Topology and Set Theory #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #math.GR

paper · pdf · doi:10.48550/arxiv.1101.2552

5 pages

arxiv created 2011/01/13 · openalex publication_date 2011/01/13 · arxiv updated 2011/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The aim of this brief note is to offer another proof of a theorem of Hrushovski that approximate subgroups of GL_n(C) are almost nilpotent. This approach generalizes to uniformly non amenable groups.

Citations

• A probabilistic technique for finding almost-periods of convolutions

Related

• Approximate groups, II: the solvable linear case
• Linear Approximate Groups
• The structure of approximate groups
• Approximate subgroups of linear groups
• Approximate groups, III: the unitary case