The hyperbolic lines of finite symplectic spaces

This problem was first suggested and discussed by Hale [6] and various special cases have been handled [ 5, 8, 121. As Hale observed, a partial linear space which is a projective plane with a point and all lines through it removed is merely the dual of an affine plane. In particular, the original projective plane can by synthetically reconstructed from the dual affine plane by the addition of a “point at infinity.” As the statement of the theorem suggests, such a partial linear space may also be thought of as the space of hyperbolic lines for a 284 0097-3165/88 $3.00