Stable group theory and approximate subgroups
Author:
Ehud Hrushovski
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
Published electronically:
June 15, 2011
MathSciNet review:
2833482
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
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 , we show that a finite subset
with
bounded is close to a finite subgroup, or else to a subset of a proper algebraic subgroup of
. 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:
ehud@math.huji.ac.il
DOI:
https://doi.org/10.1090/S0894-0347-2011-00708-X
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.
Article copyright:
© Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.