Stable group theory and approximate subgroups
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- by Ehud Hrushovski
- J. Amer. Math. Soc. 25 (2012), 189-243
- DOI: https://doi.org/10.1090/S0894-0347-2011-00708-X
- Published electronically: June 15, 2011
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Abstract:
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.References
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Bibliographic Information
- Ehud Hrushovski
- Affiliation: Institute of Mathematics, Hebrew University at Jerusalem, Giv’at Ram, 91904 Jerusalem, Israel
- Email: ehud@math.huji.ac.il
- 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: https://doi.org/10.1090/S0894-0347-2011-00708-X
- MathSciNet review: 2833482