Point Symmetric 2-Structures

We show that every symmetric 2-structure of the class (III) [cf. Karzel H et al. (Result. Math., submitted)] is point symmetric, i.e. any two orthogonal chains intersect in exactly one point and that any two points have exactly one midpoint m : = a * b (with where is the unique symmetry in the point m ). is invariant, i.e. . Therefore the pair is an invariant regular involution set and the loop derivation in a point gives a K-loop ( P , +) uniquely 2-divisible.