On subsets with small product in torsion-free groups

Combinatorica

Volumn 18, Issue 4, 1998, Pages 529-540

  Hamidoune, Y O ^a   Llado A S ^b   Serra, O ^b  

^a CNRS   (France)

^b UNIVERSITAT POLITÈCNICA DE CATALUNYA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0040096164     PISSN: 02099683     EISSN: None     Source Type: Journal    
DOI: 10.1007/s004930050038     Document Type: Article

References (12)

1. L. V. BRAILOVSKY and G. A. FREIMAN: On a product of finite subsets in a torsion-free group, J. Algebra, 130 (1990), 462-476.
2. G. FREIMAN: Structure theory of set addition, Proc. Conf. Structure theory of set addition, Marseille, Luminy June 1993, 299-318.
3. n, Proc. Conf. Number Theory, Coll. Math. Soc. J. Bolyai 51, North Holland-Bolyai Társulat, Budapest (1989), 125-139.
4. Y. O. HAMIDOUNE: An isoperimetric method in additive theory, J. Algebra, 179 (1996), 622-630.
5. Y. O. HAMIDOUNE: Some results in additive number theory, preprint, January 1997.
6. J. H. B. KEMPERMAN: On complexes in a semigroup, Indag. Math., 18 (1956), 247-254.
7. V. F. LEV and P. Y. SMELIANSKI: On addition of two distinct sets of integers, Acta Arith., 70 (1995), 85-91.
8. H. B. MANN: Addition theorems: The addition theorems of group theory and number theory, Interscience, New York, 1965.
9. M. B. NATHANSON: Additive number theory: Inverse problems and the geometry of sumsets, Springer-Verlag GTM 165, 1996.
10. I. RUZSA: Sum of sets in several dimensions, Combinatorica, 14 (1994), 485-490.
11. J. STEINIG: On Freiman's theorems concerning the sums of two finite sets of integers, Structure theory of set addition, Proc. conf. Structure theory of set addition, Marseille, Luminy (June 1993), 173-185.
12. G. VOSPER: The critical pairs of subsets of a group of prime order, J. London Math. Soc., 31 (1956), 200-205.