Keedwell's conjecture on non-extendable near transversals in group latin squares

Let $G$ be a finite non-Abelian group, and let $L(G)$ denote its latin square. A partial transversal is a collection of cells that intersects each row, column, and symbol class at most once; it is non-extendable if it is not contained in any larger partial transversal. A near transversal is a partial transversal of size $|G|-1$. Keedwell's conjecture. The latin square $L(G)$ possesses a non-extendable near transversal. The conjecture is noted as a special case of a conjecture of Keedwell concerning sequenceable groups; the paper discusses it as an extension to which its techniques may apply, and its general validity remains open.