Embeddings of generalized Latin squares in finite groups - Chen, H.V.; Chin, A.Y.M. (2015)
Let n be a positive integer. A generalized Latin square of order n is an matrix such that the elements in each row and each column are distinct. The square is said to be commutative if the matrix is symmetric. Given , we show that for any , there exists a commutative generalized Latin square of order n with m distinct elements which is embeddable in a finite group. We also show that for and for any where , there exists a non-commutative generalized Latin square of order n with m distinct elements which is embeddable in a finite group.