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- W4297066890 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. Combining these methods with Gromov's proof, we show that a finitely generated group with an approximate subgroup containing any given finite set must be nilpotent-by-finite. Model-theoretically we prove the independence theorem and the stabilizer theorem in a general first-order setting." @default.
- W4297066890 created "2022-09-26" @default.
- W4297066890 creator A5053070582 @default.
- W4297066890 date "2009-09-11" @default.
- W4297066890 modified "2023-10-16" @default.
- W4297066890 title "Stable group theory and approximate subgroups" @default.
- W4297066890 doi "https://doi.org/10.48550/arxiv.0909.2190" @default.
- W4297066890 hasPublicationYear "2009" @default.
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