Complete latin squares of order pn exist for odd primes p and n>2

AbstractA sequencing in a finite group G is a list of all elements of G such that the partial products of the list are all distinct. The existence of a sequencing in the nonabelian group of order pn which contains an element of order pn−1, where p is an odd prime and n>2, is demonstrated. It follows that complete latin squares exist for these orders. A sufficient condition for the existence of a sequencing in the nonabelian group of order pq is also given, where p