Sieve methods in group theory I: Powers in Linear groups

2011/07/19 by Alexander Lubotzky, Lubotzky, Alexander, Chen Meiri +1 · 1 citation
Mathematics · #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR) #Limits and Structures in Graph Theory

paper · pdf · doi:10.48550/arxiv.1107.3666

openalex publication_date 2011/07/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A general sieve method for groups is formulated. It enables one to "measure" subsets of a finitely generated group. As an application we show that if Γ is a finitely generated non virtually-solvable linear group of characteristic zero then the set of proper powers in Γ is exponentially small. This is a far reaching strengthening of the main result of \citeHKLS.

Citations

• Generalization of Selberg's 3/16 Theorem and Affine Sieve

Cited by

• Uniform spectral gaps, non-abelian Littlewood-Offord and anti-concentration for random walks

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