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On some classes of finite loops. (English) Zbl 0826.05011

A loop of order \(n\) is a Latin square whose first row and column consist of the integers from 1 through \(n\) appearing in their natural order. The authors continue a discussion from an earlier paper of four new equivalence classes of loops: parastrophic closures and three others that fall between isomorphic and isotopy classes of loops. They show how two of these three classes can be used to determine the isotopy classes of loops. The best possible upper bound for the cardinality of parastrophic closures is also obtained.

MSC:

05B15 Orthogonal arrays, Latin squares, Room squares
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