On finite subsets of nonabelian groups with small doubling
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- by Gregory A. Freiman PDF
- Proc. Amer. Math. Soc. 140 (2012), 2997-3002 Request permission
Abstract:
We give a detailed and clear exposition of the basic result describing the structure of a finite subset $A$ of a nonabelian group $G$ with a small doubling $|A^2| < 1.5 |A|$.References
- E. Breuillard, B. Green, Approximate groups, I: The torsion-free nilpotent case, preprint arXiv: 0906.3598vl [mathCO] 19 June 2009.
- E. Breuillard, B. Green, Approximate groups, II: The solvable linear case, preprint arXiv:0907.0927.
- E. Breuillard, B. Green, T. Tao, Approximate subgroups of linear groups, preprint.
- D. Fisher, N.H. Katz, I. Peng, On Freiman’s theorem in nilpotent groups, preprint arXiv:0901.1409vl [mathCO] 11 Jan. 2009.
- G. A. Freĭman, Groups and the inverse problems of additive number theory, Number-theoretic studies in the Markov spectrum and in the structural theory of set addition (Russian), Kalinin. Gos. Univ., Moscow, 1973, pp. 175–183 (Russian). MR 0435006
- E. Hrushovski, Stable group theory and approximate subgroups, preprint arXiv:0909.2190, 2009.
- B. Green, Approximate groups and their applications: work of Bourgain, Gamburd, Helfgott and Sarnak, preprint arXiv:0911.335vl (mathNT] 17 Nov. 2009.
- Terence Tao, Product set estimates for non-commutative groups, Combinatorica 28 (2008), no. 5, 547–594. MR 2501249, DOI 10.1007/s00493-008-2271-7
- Y. O. Hamidoune, Two inverse results, preprint arXiv:1006.5074v1, 25 June 2010.
Additional Information
- Gregory A. Freiman
- Affiliation: Department of Mathematics, Tel Aviv University, Ramat Aviv, Tel Aviv, Israel
- Email: grisha@post.tau.ac.il
- Received by editor(s): May 18, 2010
- Received by editor(s) in revised form: March 27, 2011
- Published electronically: January 13, 2012
- Communicated by: Matthew A. Papanikolas
- © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 140 (2012), 2997-3002
- MSC (2010): Primary 20-XX; Secondary 11P70
- DOI: https://doi.org/10.1090/S0002-9939-2012-11156-6
- MathSciNet review: 2917072