On finite subsets of nonabelian groups with small doubling
Author:
Gregory A. Freiman
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
Published electronically:
January 13, 2012
MathSciNet review:
2917072
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Abstract | References | Similar Articles | Additional Information
Abstract: We give a detailed and clear exposition of the basic result describing the structure of a finite subset of a nonabelian group
with a small doubling
.
- 1. E. Breuillard, B. Green, Approximate groups, I: The torsion-free nilpotent case, preprint arXiv: 0906.3598vl [mathCO] 19 June 2009.
- 2. E. Breuillard, B. Green, Approximate groups, II: The solvable linear case, preprint arXiv:0907.0927.
- 3. E. Breuillard, B. Green, T. Tao, Approximate subgroups of linear groups, preprint.
- 4. D. Fisher, N.H. Katz, I. Peng, On Freiman's theorem in nilpotent groups, preprint arXiv:0901.1409vl [mathCO] 11 Jan. 2009.
- 5. 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
- 6. E. Hrushovski, Stable group theory and approximate subgroups, preprint arXiv:0909.2190, 2009.
- 7. B. Green, Approximate groups and their applications: work of Bourgain, Gamburd, Helfgott and Sarnak, preprint arXiv:0911.335vl (mathNT] 17 Nov. 2009.
- 8. Terence Tao, Product set estimates for non-commutative groups, Combinatorica 28 (2008), no. 5, 547–594. MR 2501249, https://doi.org/10.1007/s00493-008-2271-7
- 9. Y. O. Hamidoune, Two inverse results, preprint arXiv:1006.5074v1, 25 June 2010.
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Additional Information
Gregory A. Freiman
Affiliation:
Department of Mathematics, Tel Aviv University, Ramat Aviv, Tel Aviv, Israel
Email:
grisha@post.tau.ac.il
DOI:
https://doi.org/10.1090/S0002-9939-2012-11156-6
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
Article copyright:
© Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.