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Mathematics of Computation

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Factoring elementary groups of
prime cube order into subsets


Authors: Sándor Szabó and Coburn Ward
Journal: Math. Comp. 67 (1998), 1199-1206
MSC (1991): Primary 20K01; Secondary 52C22
DOI: https://doi.org/10.1090/S0025-5718-98-00929-6
MathSciNet review: 1451328
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Abstract: Let $p$ be a prime and let $G$ be the $3$-fold direct product of the cyclic group of order $p$. Rédei conjectured if $G$ is the direct product of subsets $A$ and $B$, each of which contains the identity element of $G$, then either $A$ or $B$ does not generate all of $G$. The paper verifies Rédei's conjecture for $p\leq 11$.


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Additional Information

Sándor Szabó
Affiliation: Department of Mathematics, University of Bahrain, ISA Town, State of Bahrain
Address at time of publication: General Science and Mathematics Department, College of Health Sciences, Manama, State of Bahrain

Coburn Ward
Affiliation: Department of Mathematics, University of the Pacific, Stockton, California 95211
Email: cward@uop.edu

DOI: https://doi.org/10.1090/S0025-5718-98-00929-6
Keywords: Factorization of groups, Latin squares
Received by editor(s): June 17, 1994
Received by editor(s) in revised form: January 23, 1997
Article copyright: © Copyright 1998 American Mathematical Society