Non-commutative generalized Latin squares of order 5 with certain number of distinct elements

Abstract

Let n be a positive integer. A generalized Latin square of order n is an n × n matrix such that the elements in each row and each column are distinct. In this paper, we shall investigate classes of non-commutative generalized Latin squares of order 5 with 5, 24, and 25 distinct elements. In addition, we shall divide the squares into equivalence classes and determine completely the squares which are embeddable in groups.