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Transactions of the American Mathematical Society

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Order evaluation of products of subsets in
finite groups and its applications. II


Authors: Z. Arad and M. Muzychuk
Journal: Trans. Amer. Math. Soc. 349 (1997), 4401-4414
MSC (1991): Primary 20D99, 05A99; Secondary 05C25
DOI: https://doi.org/10.1090/S0002-9947-97-01866-7
MathSciNet review: 1407477
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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we give a new estimate of the cardinality of the product of subsets $AB$ in a finite non-abelian simple group, where $A$ is normal and $B$ is arbitrary. This estimate improves the one given in J. Algebra 182 (1996), 577-603.


References [Enhancements On Off] (What's this?)

  • 1. Z.Arad, H.Blau, On table algebras and their applications to finite group theory, J. Algebra, 138 (1991), 137-185. MR 92f:20007
  • 2. Z.Arad, E.Fisman, M.Muzychuk. Order evaluation of products of subsets in finite groups and its applications.I, J. Algebra 182 (1996), 577-603. CMP 96:15
  • 3. I.D.Dixon, B. Mortimer. The primitive permutation groups of degree less than 1000, Math. Proc. Camb. Phil. Soc., 103 (1988), 213-238. MR 89b:20014
  • 4. W.Feit. Characters of Finite Groups, Benjamin, New York, Amsterdam, 1967. MR 36:2715
  • 5. W.Feit and J.Thompson. Finite groups which contain a self-centralizing subgroup of order 3. Nagoya Math. J. 21, (1962), pp. 185-197. MR 26:192
  • 6. B.Huppert, N.Blackburn, Finite groups II, Springer-Verlag, 1982. MR 84i:20001a
  • 7. I.M.Isaacs and Ilan Zisser. Squares of characters with a few constituents in finite groups. Arch. Math. 63, 1994, pp. 197-207. MR 95e:20015
  • 8. B.A.Pogorelov, Primitive groups of permutations of small degrees. II, Algebra i Logika, 19 1980, n.4, pp. 423-457. MR 82j:20009b

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Additional Information

Z. Arad
Affiliation: Department of Mathematics & Computer Science, Bar-Ilan University, 52900 Ramat-Gan, Israel

M. Muzychuk
Affiliation: Department of Mathematics & Computer Science, Bar-Ilan University, 52900 Ramat-Gan, Israel

DOI: https://doi.org/10.1090/S0002-9947-97-01866-7
Received by editor(s): September 25, 1995
Additional Notes: This work was done at the Gelbart and Emmy Noether Research Institutes for Mathematical Sciences at Bar-Ilan University.
The second author was supported by the research grants from the Israeli Ministry of Science and the German-Israeli Foundation for fundamental research.
Article copyright: © Copyright 1997 American Mathematical Society

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