Sieve methods in group theory I: Powers in Linear groups

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 $\Gamma$ is a finitely generated non virtually-solvable linear group of characteristic zero then the set of proper powers in $\Gamma$ is exponentially small. This is a far reaching strengthening of the main result of \cite{HKLS}.

33 pages, 4 figures

References in corpus (2)

• Growth in finite simple groups of Lie type of bounded rank
• Approximate subgroups of linear groups

Cited by in corpus (1)

• Sieve methods in group theory \Rmnum{3}: $\aut(F_n)$