The structure of approximate groups

@article{Breuillard2011TheSO,
  title={The structure of approximate groups},
  author={E. Breuillard and B. Green and T. Tao},
  journal={Publications math{\'e}matiques de l'IH{\'E}S},
  year={2011},
  volume={116},
  pages={115-221}
}
Let K⩾1 be a parameter. A K-approximate group is a finite set A in a (local) group which contains the identity, is symmetric, and such that A⋅A is covered by K left translates of A.The main result of this paper is a qualitative description of approximate groups as being essentially finite-by-nilpotent, answering a conjecture of H. Helfgott and E. Lindenstrauss. This may be viewed as a generalisation of the Freiman-Ruzsa theorem on sets of small doubling in the integers to arbitrary groups.We… Expand
128 Citations
The Structure of Locally Compact Approximate Groups
  • 9
  • PDF
Additive problems in abelian groups
  • PDF
Kneser-type Theorems for countable amenable groups
  • PDF
Approximate lattices
  • 18
  • PDF
Nilprogressions and groups with moderate growth
  • 29
  • PDF
Approximate subgroups of residually nilpotent groups
  • 4
  • Highly Influenced
  • PDF
Beyond the Lascar Group.
  • 2
  • Highly Influenced
  • PDF
Approximate subgroups with bounded VC-dimension
  • Highly Influenced
  • PDF
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 72 REFERENCES
Freiman's theorem for solvable groups
  • T. Tao
  • Mathematics, Computer Science
  • Contributions Discret. Math.
  • 2010
  • 43
  • PDF
An analog of Freiman's theorem in groups
  • 107
  • Highly Influential
Groups Without Small Subgroups
  • 140
  • Highly Influential
A Generalization of A Theorem of Gleason
  • 109
  • Highly Influential
Growth in finite simple groups of Lie type of bounded rank
  • 124
  • PDF
Gromov's theorem on groups of polynomial growth and elementary logic
  • 199
  • PDF
A Probabilistic Technique for Finding Almost-Periods of Convolutions
  • 75
  • PDF
Stable group theory and approximate subgroups
  • 149
  • Highly Influential
  • PDF
On the Conjecture of Iwasawa and Gleason
  • 51
  • Highly Influential
Lie Algebras and Lie Groups
  • 229
...
1
2
3
4
5
...