Geodesic
ON MULTIPLICATION TABLES OF GROUPS THAT AGREE ON HALF OF THE COLUMNS AND HALF OF THE ROWS
Glasgow mathematical journal, Tome 45 (2003) no. 2, pp. 293-308

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DOI

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.
DOI : 10.1017/S0017089503001253
Mots-clés : 20D60, 05B15 
DRÁPAL, ALEš; ZHUKAVETS, NATALIA. ON MULTIPLICATION TABLES OF GROUPS THAT AGREE ON HALF OF THE COLUMNS AND HALF OF THE ROWS. Glasgow mathematical journal, Tome 45 (2003) no. 2, pp. 293-308. doi: 10.1017/S0017089503001253
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     author = {DR\'APAL, ALE\v{s} and ZHUKAVETS, NATALIA},
     title = {ON {MULTIPLICATION} {TABLES} {OF} {GROUPS} {THAT} {AGREE} {ON} {HALF} {OF} {THE} {COLUMNS} {AND} {HALF} {OF} {THE} {ROWS}},
     journal = {Glasgow mathematical journal},
     pages = {293--308},
     year = {2003},
     volume = {45},
     number = {2},
     doi = {10.1017/S0017089503001253},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089503001253/}
}
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