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Some Constructions of Non-Commutative Latin Squares of Order n

Authors: H. V. Chen, A. Y. M. Chin, S. Sharmini


Let n be an integer. We show the existence of at least three non-isomorphic non-commutative Latin squares of order n which are embeddable in groups when n ≥ 5 is odd. By using a similar construction for the case when n ≥ 4 is even, we show that certain non-commutative Latin squares of order n are not embeddable in groups.

Keywords: Group, embedding, Latin square

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