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.

38 pages, no figures. Some corrections

References in corpus (2)

• Growth and generation in SL_2(Z/pZ)
• Compressions, convex geometry and the Freiman-Bilu theorem

Cited by in corpus (5)

• Freiman's theorem for solvable groups
• The sum-product phenomenon in arbitrary rings
• Growth in SL_3(Z/pZ)
• A finitary version of Gromov's polynomial growth theorem
• On Freiman's Theorem in Nilpotent Groups