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Product set estimates for noncommutative groups
 Combinatorica
"... Abstract. We develop the PlünneckeRuzsa and BalogSzemerédiGowers theory of sum set estimates in the noncommutative setting, with discrete, continuous, and metric entropy formulations of these estimates. We also develop a Freimantype inverse theorem for a special class of 2step nilpotent groups ..."
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Cited by 17 (3 self)
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Abstract. We develop the PlünneckeRuzsa and BalogSzemerédiGowers theory of sum set estimates in the noncommutative setting, with discrete, continuous, and metric entropy formulations of these estimates. We also develop a Freimantype inverse theorem for a special class of 2step nilpotent groups, namely the Heisenberg groups with no 2torsion in their vertical group. 1.
Stable group theory and approximate subgroups
 J. Amer. Math. Soc
"... Abstract. We note a parallel between some ideas of stable model theory and certain topics in finite combinatorics related to the sumproduct phenomenon. For a simple linear group G, we show that a finite subset X with XX −1 X/X  bounded is close to a finite subgroup, or else to a subset of a pro ..."
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Cited by 9 (0 self)
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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 sumproduct phenomenon. For a simple linear group G, we show that a finite subset X with XX −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. Modeltheoretically we prove the independence theorem and the stabilizer theorem in a general firstorder setting. 1.