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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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Sieve methods in group theory I: Powers in linear groups
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by Alexander Lubotzky and Chen Meiri PDF
J. Amer. Math. Soc. 25 (2012), 1119-1148 Request permission

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 generalization of a result of Hrushovski, Kropholler, Lubotzky, and Shalev.
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Additional Information
  • Alexander Lubotzky
  • Affiliation: Einstein Institute of Mathematics, Hebrew University, Jerusalem 90914, Israel
  • MR Author ID: 116480
  • Email: alexlub@math.huji.ac.il
  • Chen Meiri
  • Affiliation: Einstein Institute of Mathematics, Hebrew University, Jerusalem 90914, Israel
  • Address at time of publication: Institute for Advanced Study, Princeton, New Jersey 08540
  • Email: chen7meiri@gmail.com
  • Received by editor(s): July 19, 2011
  • Received by editor(s) in revised form: January 20, 2012
  • Published electronically: April 11, 2012
  • © Copyright 2012 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: J. Amer. Math. Soc. 25 (2012), 1119-1148
  • MSC (2010): Primary 20Pxx
  • DOI: https://doi.org/10.1090/S0894-0347-2012-00736-X
  • MathSciNet review: 2947947