New results on subset multiplication in groups
Structure theory of set addition, Astérisque no. 258  (1999), p. 309-315
@incollection{AST_1999__258__309_0,
     author = {Herzog, Marcel},
     title = {New results on subset multiplication in groups},
     booktitle = {Structure theory of set addition},
     editor = {Deshouilliers Jean-Marc and Landreau Bernard and Yudin Alexander A.},
     series = {Ast\'erisque},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {258},
     year = {1999},
     pages = {309-315},
     zbl = {0944.20019},
     mrnumber = {1701205},
     language = {en},
     url = {http://www.numdam.org/item/AST_1999__258__309_0}
}
Herzog, Marcel. New results on subset multiplication in groups, in Structure theory of set addition, Astérisque, no. 258 (1999), pp. 309-315. http://www.numdam.org/item/AST_1999__258__309_0/

[1] Babai L. and Sós V. T., Sidon sets in groups and induced subgraphs of Cayley graphs, Europ. J. Combinatorics, 6, 1985, 101-114 | Article | MR 810691 | Zbl 0573.05032

[2] Berkovich Ja. G., Freiman G. A. and Praeger C. E., Small squaring and cubing properties for finite groups, Bull. Austral. Math. Soc., 44, 1991, 429-450 | Article | MR 1138020 | Zbl 0728.20020

[3] Bertram E. A. and Herzog M., On medium-size subgroups and bases of finite groups, J. of Combin. Theory, Series A, 57, 1991, 1-14 | Article | MR 1101744 | Zbl 0744.20028

[4] Brailovsky L., A characterization of abelian groups, Proc. Amer. Math. Soc., 117, 1993, no. 3, 627-629. | Article | MR 1129873 | Zbl 0789.20022

[5] Brailovsky L., On the small squaring and commutativity, Bull. London Math. Soc., 25, 1993, 330-336. | Article | MR 1222724 | Zbl 0795.20012

[6] Brailovsky L., Combinatorial conditions forcing commutativity of an infinite group, J. of Algebra, 165, 1994, no. 2, 394-400. | Article | MR 1273282 | Zbl 0812.20014

[7] Finkelstein L., Kleitman D. and Leighton T., Applying the classification theorem for finite simple groups to minimize pin count in uniform permutation architectures, VLSI algorithms and architectures, J.H. Reif(ed), Springer, 1989, 247-256 | MR 1017477 | Zbl 0659.20012

[8] Freiman G. A., On two and three-element subsets of groups Aeq. Math., 22, 1981, 140-152 | Article | MR 645414 | Zbl 0489.20020

[9] Herzog M., Longobardi P. and Maj M., On a combinatorial problem in group theory, Israel J. Math., 82, 1993, no. 1-3, 329-340. | Article | MR 1239053 | Zbl 0794.20041

[10] Herzog M. and Menegazzo F., On deficient products in infinite groups, Rend. Sem. Mat. Univ. Padova, 93, 1995, 1-6. | Numdam | MR 1354347 | Zbl 0839.20042

[11] Herzog M. and Scoppola C. M., On deficient squares groups and fully-independent subsets Bull. London Math. Soc., 27, 1995, no. 1, 65-70. | Article | MR 1331683 | Zbl 0827.20045

[12] Jia X-D., Thin bases for abelian groups, J. Number Theory, 36, 1990, 254-256 | Article | MR 1072469 | Zbl 0711.11007

[13] Jia X-D., Thin bases for finite nilpotent groups, J. Number Theory, 41, 1992, 303-313 | Article | MR 1168990 | Zbl 0758.11006

[14] Kilian J., Kipnis S. and Leierson Ch. E., The organization of permutation architectures with bussed interconnections, Proc. 1987 IEEE Conf. On The Foundation Of Comp. Science, IEEE, 1987, 305-315

[15] Kozma G. and Lev A., Bases and decomposition numbers of finite groups, Arch. Math., 58, 1992, 417-424 | Article | MR 1156573 | Zbl 0724.11005

[16] Kozma G. and Lev A., On h-bases and h-decompositions of the finite solvable and alternating groups, J. Number Theory, 49, 1994, no. 3, 385-391 | Article | MR 1307974 | Zbl 0815.11009

[17] Lennox J. C., Hassanabadi A. M. and Wiegold J., Some commutativity criteria, Rend. Sem. Mat. Univ. Padova, 84, 1990, 135-141 | Numdam | MR 1101288 | Zbl 0725.20025

[18] Lev A., On large subgroups of finite groups, J. of Algebra, 152, 1992, 434-438 | Article | MR 1194312 | Zbl 0769.20011

[19] Longobardi P. and Maj M., The classification of groups with the small-squaring property on 3-sets, Bull. Austral Math. Soc., 46, 1992, 263-269 | Article | MR 1183782 | Zbl 0780.20014

[20] Menegazzo F., A property equivalent to commutativity for infinite groups Rend. Sem. Mat. Univ. Padova, 87, 1992, 299-301 | Numdam | MR 1183913 | Zbl 0812.20015

[21] Neumann B. H., A problem of Paul Erdös on groups, J. Austral. Math. Soc., 21, 1976, 467-472, Selected works of B.H.Neumann and Hanna Neumann, 5, 1003-1008 | Article | MR 419283 | Zbl 0333.05110

[22] Neumann P. M., A combinatorial problem in group theory, Private communication. | Zbl 0695.20018

[23] Rohrbach H., Anwendung eines Satzes der additiven Zahlentheorie auf eine gruppenthe-oretishe Frage, Math. Z., 42, 1937, 538-542 | Article | JFM 63.0066.02 | MR 1545690