On the number of transversals in a class of Latin squares

Abstract Denote by A p k the Latin square of order n = p k formed by the Cayley table of the additive group ( Z p k , + ) , where p is an odd prime and k is a positive integer. It is shown that for each p there exists Q > 0 such that for all sufficiently large k , the number of transversals in A p k exceeds ( n Q ) n p ( p − 1 ) .