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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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Stable group theory and approximate subgroups
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by Ehud Hrushovski PDF
J. Amer. Math. Soc. 25 (2012), 189-243 Request permission


We note a parallel between some ideas of stable model theory and certain topics in finite combinatorics related to the sum-product phenomenon. For a simple linear group $G$, we show that a finite subset $X$ with $|X X ^{-1}X |/ |X|$ bounded is close to a finite subgroup, or else to a subset of a proper algebraic subgroup of $G$. We also find a connection with Lie groups, and use it to obtain some consequences suggestive of topological nilpotence. Model-theoretically we prove the independence theorem and the stabilizer theorem in a general first-order setting.
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Additional Information
  • Ehud Hrushovski
  • Affiliation: Institute of Mathematics, Hebrew University at Jerusalem, Giv’at Ram, 91904 Jerusalem, Israel
  • Email:
  • Received by editor(s): August 24, 2010
  • Received by editor(s) in revised form: May 16, 2011
  • Published electronically: June 15, 2011
  • Additional Notes: Research supported in part by Israel Science Foundation grant 1048/07.
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: J. Amer. Math. Soc. 25 (2012), 189-243
  • MSC (2010): Primary 11P70, 03C45
  • DOI:
  • MathSciNet review: 2833482