The Uniqueness of the 1-System of Q−(7, q), q Odd

It is known that every m-system of the elliptic polar space Q−(2n+1, q) is an SPG regulus of the ambient space PG(2n+1, q) of Q−(2n+1, q). From the proof of this result, applied to 1-systems of Q−(7, q), it follows that for q odd, each plane of Q−(7, q) either contains a line of the 1-system or an irreducible conic of points on lines of the 1-system. This observation is used to show that Q−(7, q) has a unique 1-system if q is odd.