Sieve methods in group theory I: Powers in Linear groups

Alexander Lubotzky; Chen Meiri

Sieve methods in group theory I: Powers in Linear groups

Group Theory 2011-07-20 v1

Authors: Alexander Lubotzky , Chen Meiri

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}.

Keywords

group theory finite group theory wreath product of groups

Cite

@article{arxiv.1107.3666,
  title  = {Sieve methods in group theory I: Powers in Linear groups},
  author = {Alexander Lubotzky and Chen Meiri},
  journal= {arXiv preprint arXiv:1107.3666},
  year   = {2011}
}

Comments

33 pages, 4 figures

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