Sieve methods in group theory I: Powers in Linear groups

Details Sieve methods in group theory I: Powers in Linear groups Sieve methods in group theory I: Powers in Linear groups

2011-07-19

arxiv.org/abs/1107.3666v1

Mathematics

Group Theory

33 pages, 4 figures

Scientific paper

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}.

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