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Verifying a conjecture of L. Rédei for $ p=13$


Author: Sándor Szabó
Journal: Math. Comp. 80 (2011), 1155-1162
MSC (2010): Primary 20K01; Secondary 05B45, 52C22, 68R05
Published electronically: September 17, 2010
MathSciNet review: 2772117
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Abstract: In 1970 L. Rédei conjectured that if an elementary $ p$-group $ G$ of order $ p^3$ is a direct product of its subsets $ A$ and $ B$ such that both $ A$ and $ B$ contain the identity element of $ G$, then at least one of the factors $ A$ and $ B$ cannot span the whole $ G$. We will verify this conjecture for $ p=13$.


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Additional Information

Sándor Szabó
Affiliation: Institute of Mathematics and Informatics, University of Pécs, Ifjúság u. 6, 7624 Pécs, Hungary
Email: sszabo7@hotmail.com

DOI: https://doi.org/10.1090/S0025-5718-2010-02417-2
Keywords: Factorization of finite abelian groups, periodic subset, full-rank factorization
Received by editor(s): September 1, 2009
Received by editor(s) in revised form: February 4, 2010
Published electronically: September 17, 2010
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.