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Preprint Number 204
204. Ehud Hrushovski Stable group theory and approximate subgroups E-mail: Submission date: 21 September 2009. 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. Mathematics Subject Classification: Keywords and phrases: |

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