On small subset product in a group
Structure theory of set addition, Astérisque, no. 258 (1999), pp. 281-308 
@incollection{AST_1999__258__281_0,
     author = {Hamidoune, Yahya Ould},
     title = {On small subset product in a group},
     booktitle = {Structure theory of set addition},
     editor = {Deshouilliers Jean-Marc and Landreau Bernard and Yudin Alexander A.},
     series = {Ast\'erisque},
     pages = {281--308},
     year = {1999},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {258},
     mrnumber = {1701204},
     zbl = {0945.20011},
     language = {en},
     url = {https://www.numdam.org/item/AST_1999__258__281_0/}
}
TY  - CHAP
AU  - Hamidoune, Yahya Ould
TI  - On small subset product in a group
BT  - Structure theory of set addition
AU  - Collectif
ED  - Deshouilliers Jean-Marc
ED  - Landreau Bernard
ED  - Yudin Alexander A.
T3  - Astérisque
PY  - 1999
SP  - 281
EP  - 308
IS  - 258
PB  - Société mathématique de France
UR  - https://www.numdam.org/item/AST_1999__258__281_0/
LA  - en
ID  - AST_1999__258__281_0
ER  - 
%0 Book Section
%A Hamidoune, Yahya Ould
%T On small subset product in a group
%B Structure theory of set addition
%A Collectif
%E Deshouilliers Jean-Marc
%E Landreau Bernard
%E Yudin Alexander A.
%S Astérisque
%D 1999
%P 281-308
%N 258
%I Société mathématique de France
%U https://www.numdam.org/item/AST_1999__258__281_0/
%G en
%F AST_1999__258__281_0
Hamidoune, Yahya Ould. On small subset product in a group, dans Structure theory of set addition, Astérisque, no. 258 (1999), pp. 281-308. https://www.numdam.org/item/AST_1999__258__281_0/

[1] Brailowski L. V. and Freiman G. A., On a product of finite subsets in a torsion free group, J. Algebra, 130, 1990, 462-476. | MR | Zbl | DOI

[2] Cauchy A., Recherches sur les nombres, J. Ecole Polytechnique, 9, 1813, 99-116.

[3] Cherly J. and Deshouillers J-M., Un théorème d'addition dans F q [X], J. Number Theory, 34, 128-131. | MR | Zbl | DOI

[4] Chowla S., Mann H. B. and Strauss L. G., Some applications of the Cauchy-Davenport theorem, Norske Vid. Selsk. Forh. (Trondheim), 32, 1959, 74-80. | MR | Zbl

[5] Davenport H., On the addition of residue classes, J. London Math. Soc., 10, 1935, 30-32. | JFM | DOI

[6] Davenport H. and Lewis D. J., Notes on congruences (III), Quart. Math. Oxford, (2) 17, 1966, 339-344. | MR | Zbl | DOI

[7] Diderrich G. T., On Kneser's addition theorem in groups, Proc. Amer. Math. Soc., 1973, 443-451. | MR | Zbl

[8] Halberstam H., and Roth K. F., Sequences, Springer-Verlag, 1982. | MR | Zbl

[9] Hamidoune Y. O., Sur les atomes d'un graphe orienté, C.R. Acad. Sc. Paris A, 284, 1977, 1253-1256. | MR | Zbl

[10] Hamidoune Y. O., Quelques problèmes de connexité dans les graphes orientés, J. Comb. Theory B, 30, 1981, 1-10. | MR | Zbl | DOI

[11] Hamidoune Y. O., An application of connectivity Theory in graphs to factorizations of elements in groups, Europ. J. Combinatorics, 2, 1981, 349-355. | MR | Zbl | DOI

[12] Hamidoune Y. O., On the connectivity of Cayley digraphs, Europ. J. Combinatorics, 5, 1984, 309-312. | MR | Zbl | DOI

[13] Hamidoune Y. O., On a subgroup contained in words with a bounded length, Discrete Math., 103, 1992, 171-176. | MR | Zbl | DOI

[14] Hamidoune Y. O., On subsets with a small sum in abelian groups, Europ. J. of Combinatorics, 18, 1997, 541-566. | MR | Zbl | DOI

[15] Hamidoune Y. O. and Rödseth Ö. J., On bases for σ-finite groups, Math. Scand., 1994, 246-254. | MR | Zbl | EuDML

[16] Hamidoune Y. O., Llàdo A. S. and Serra O., Vosperian and superconnected abelian Cayley digraphs, Graphs and Combinatorics, 7, 1991, 143-152. | MR | Zbl | DOI

[17] Jia X. B. and Nathanson M. B., Additions theorems for σ-finite groups, In Proc. Rademacher Centenary conference, contemporary mathematics, Amer math. Soc. 1194. | MR | Zbl

[18] Jung H. A., Über den Zusammenhang von Graphen, mit Anwendungen auf symmetricher Graphen, Math. Ann., 202, 1973, 307-320. | MR | Zbl | EuDML | DOI

[19] Kempermann J. H. B., On complexes in a semigroup, Indag. Math., 18, 1956, 247-254. | MR | Zbl | DOI

[20] Kempermann J. H. B., On small sumsets in abelian groups, Acta Math., 103, 1960, 66-88. | MR | Zbl

[21] Kneser M., Anwendung eines satzes von Mann auf die Geometrie von Zahlen, Proc. Int. Cong. Math. Amsterdam, 2, 1954, 32.

[22] Kneser M., Eine Satz über abelesche gruppen mit Anwendungen auf die Geometrie der Zahlen, Math. Z., 1955, 429-434. | MR | Zbl | EuDML

[23] Mader W., Eine Eigenschaft der Atome endlicher Graphen, Arch. Math., 22, 1971, 333-336. | MR | Zbl | DOI

[24] Mann H. B., An addition theorem for sets of elements of an abelian group, Proc. Amer. Math Soc, 4, 1953, 423. | Zbl | MR

[25] Mann H. B., Addition theorems : The addition theorems of group theory and number theory, Interscience, New York, 1965. | MR | Zbl

[26] Nathanson M. B., Additive number theory : Inverse problems and the Geometry of sum-sets, Springer-Verlag, 1994, to appear. | Zbl | MR

[27] Olson J. E., On the sum of of two sets in a group, J. Number Theory, 18, 1984, 110-120. | MR | Zbl | DOI

[28] Olson J. E., On the symmetric difference of two sets in a group, Europ. J. Combinatorics, 1986, 43-54. | MR | Zbl | DOI

[29] Rödseth Ö. J., Two remarks on linear forms in non-negative integers, Math. Scand., 51, 1982, 193-198. | MR | Zbl | EuDML | DOI

[30] Tietäväinen A., On diagonal forms over finite fields, Ann. Univ. Turku Ser. A, 1968, 1-10. | MR | Zbl

[31] Vosper G., The critical pairs of subsets of a group of prime order, J. London Math. Soc., 31, 1956, 200-205. | MR | Zbl | DOI

[32] Vosper G., Addendum to "The critical pairs of subsets of a group of prime order", J. London Math. Soc., 31, 1956, 280-282. | MR | Zbl | DOI

[33] Zemor G., A generalisation to noncommutative groups of a theorem of Mann, Discrete Math., 126, 1994, 365-372. | MR | Zbl | DOI