---
tag: 51P4QCXZHC
kind: statement
role: theorem
name: Breuillard–Green–Tao theorem
sources:
  - wikipedia: en:18243381@r1351196394
    locator: Arithmetic combinatorics, section Important results > Breuillard–Green–Tao theorem
    note: adopted
    mention: wikipedia://en/18243381#70Z5
    sections: [Statement]
inventory: [7S1729H599]
---

## Statement

The Breuillard–Green–Tao theorem, proved by Emmanuel Breuillard, Ben Green, and Terence Tao in 2011, gives a complete classification of approximate groups. This result can be seen as a nonabelian version of Freiman's theorem, and a generalization of Gromov's theorem on groups of polynomial growth.