Freiman's theorem in an arbitrary abelian group

Journal of the London Mathematical Society

Volumn 75, Issue 1, 2007, Pages 163-175

  Green, Ben ^a   Ruzsa, Imre Z ^b  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

^b INSTITUTE OF EXPERIMENTAL MEDICINE   (Hungary)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 38949176568     PISSN: 00246107     EISSN: 14697750     Source Type: Journal    
DOI: 10.1112/jlms/jdl021     Document Type: Article

References (14)

1. Y. BILU, 'Structure of sets with small sumset', Structure theory of set addition, Astérisque 258 (Société Mathématique de France, Paris, 1999) 77-108.
2. N. N. BOGOLYUBOV, 'Sur quelques propriétés arithmétiques des presque-périodes', Ann. Chaire Math. Phys. Kiev 4 (1939) 185-194.
3. J. W. S. CASSELS, 'An introduction to the geometry of numbers', corrected reprint of the 1971 edition. Classics in mathematics (Springer, Berlin, 1997).
4. M. C. CHANG, 'A polynomial bound in Freiman's theorem', Duke Math. J. 113 (2002) 399-419.
5. n', Combinatorica 24 (2004) 53-68.
6. G. FREIMAN, Foundations of a structural theory of set addition, Translations of Mathematical Monographs 37 (American Mathematical Society, Providence, RI, 1973).
7. B. J. GREEN, 'Edinburgh-MIT lecture notes on Freiman's theorem', Preprint, 2006, http://www.dpmms.cam.ac.uk/~bjg23.
8. B. J. GREEN and I. Z. RUZSA, 'Sets with small sumset and rectification', Bull. London Math. Soc., 38 (2006) 43-52.
9. H. PLÜNNECKE, Eigenschaften un Abschätzungen von Wirkingsfunktionen, BMwF-GMD-22 (Gesellschaft für Mathematik und Datenverarbeitung, Bonn, 1969).
10. W. RUDIN, Fourier analysis on groups, Interscience Tracts in Pure and Applied Mathematics 12 (Wiley-Interscience, New York, 1962).
11. I. Z. RUZSA, 'On the cardinality of A + A and A - A', Proc. Fifth Hungarian Colloquium on Combinatorics, Keszthely, 1976, Vol. II, Colloquia Mathematica Societatis János Bolyai 18 (North-Holland, Amsterdam, 1978) 933-938.
12. I. Z. RUZSA, 'An application of graph theory to additive number theory', Sci. Ser. A Math. Sci. (N.S.) 3 (1989) 97-109.
13. I. Z. RUZSA, 'Generalized arithmetical progressions and sumsets', Acta Math. Hungar. 65 (1994) 379-388.
14. I. Z. RUZSA, 'An analog of Freiman's theorem in groups', Structure theory of set addition, Astérisque 258 (Société Mathématique de France, Paris, 1999) 323-326.