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 in a finite non-abelian simple group, where is normal and is arbitrary. This estimate improves the one given in J. Algebra 182 (1996), 577-603.

**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