Product set estimates for non-commutative groups

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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Correspondence to Terence Tao.

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T. Tao is supported by a grant from the Packard Foundation.

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Tao, T. Product set estimates for non-commutative groups. Combinatorica 28, 547–594 (2008). https://doi.org/10.1007/s00493-008-2271-7

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Mathematics Subject Classification (2000)

  • 11P70