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ON MULTIPLICATION TABLES OF GROUPS THAT AGREE ON HALF OF THE COLUMNS AND HALF OF THE ROWS

Published online by Cambridge University Press:  01 August 2003

ALEš DRÁPAL  and
NATALIA ZHUKAVETS
ALEš DRÁPAL
Affiliation:
Department of Mathematics and Physics (MFF), Karlova (Charles) University (UK), 18675 Prague 8, Czech Republic e-mail: drapal@karlin.mff.cuni.cz
NATALIA ZHUKAVETS
Affiliation:
Department of Mathematics and Physics (MFF), Karlova (Charles) University (UK), 18675 Prague 8, Czech Republic
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Abstract

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Let $G(o)$ and $G(*)$ be two groups of finite order $n$, and suppose that each of the sets $\{u\in G;\ uo v=u*v$ for all $v\in G\}$ and $\{v\in G;\ uo v=u*v$ for all $u\in G\}$ has $n/2$ elements. Then $G(*)$ can be obtained from $G(o)$ by one of the two general constructions that are discussed in the paper.

Keywords

20D6005B15
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 45 , Issue 2 , May 2003 , pp. 293 - 308
Copyright
2003 Glasgow Mathematical Journal Trust