On completing three cyclically generated transversals to a latin square

AbstractLet P be a partial latin square of prime order p>7 consisting of three cyclically generated transversals. Specifically, let P be a partial latin square of the form:P={(i,c+i,s+i),(i,c′+i,s′+i),(i,c″+i,s″+i)|0⩽i<p} for some distinct c,c′,c″ and some distinct s,s′,s″. In this paper we show that any such P completes to a latin square which is diagonally cyclic. Equivalently, we prove that for each prime p>7, every partial transversal of size 3 in the addition table for the integers modulo p can be completed to a full transversal