Latin squares in a Cayley table

Abstract

Let G be a finite group of order n ≥ 2 and T be the Cayley table of G. Obviously T is a Latin square. In this paper we study submatrices of T which are Latin squares. Let Lm(G) where m ≤ n be the number of Latin squares of order m in T. We compute Lm(G) and study some properties of such submatrices. Also we classify the Latin squares of order m in T and compute the number of each classes in some cases.