Geodesic
A class of latin squares derived from finite abelian groups
Commentationes Mathematicae Universitatis Carolinae, Tome 55 (2014) no. 3, pp. 401-409.

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We consider two classes of latin squares that are prolongations of Cayley tables of finite abelian groups. We will show that all squares in the first of these classes are confirmed bachelor squares, squares that have no orthogonal mate and contain at least one cell though which no transversal passes, while none of the squares in the second class can be included in any set of three mutually orthogonal latin squares.
Classification : 05B15
Keywords: latin squares; bachelor squares; monogamous squares; prolongation 
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     title = {A class of latin squares derived from finite abelian groups},
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Evans, Anthony B. A class of latin squares derived from finite abelian groups. Commentationes Mathematicae Universitatis Carolinae, Tome 55 (2014) no. 3, pp. 401-409. http://geodesic.mathdoc.fr/item/CMUC_2014__55_3_a8/