A constraint on the biembedding of Latin squares

We give a necessary condition for the biembedding of two Latin squares in an orientable surface. As a consequence, it is shown that for n >= 2, there is no biembedding of two Latin squares both lying in the same main class as the square obtained from the Cayley table of the Abelian 2-group C(2)(n). (C) 2008 Published by Elsevier Lt