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Product set estimates for non-commutative groups

Terence Tao
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Abstract

We develop the Plünnecke-Ruzsa and Balog-Szemerédi-Gowers theory of sum set estimates in the non-commutative setting, with discrete, continuous, and metric entropy formulations of these estimates. We also develop a Freiman-type inverse theorem for a special class of 2-step nilpotent groups, namely the Heisenberg groups with no 2-torsion in their centre.

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Terence Tao. 2011-10-26. Product set estimates for non-commutative groups. https://arxiv.org/abs/math/0601431

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