ABSTRACT
Andre´ translation planes may be regarded as a far-reaching generalization of the Hall planes and the Desarguesian planes. They exist for any strict prime power n = pd > p, and although they are never (proper) semifield planes, the class of of Andre´ planes overlaps the class of nearfield planes-neither class includes the other. Thus, for more than two decades the Andre´ planes included the only known class of projective planes (up to duality) of non-square order that are not nearfield or semifield planes. This remained the situation until Foulser in 1967 [369] constructed his λ-planes, which include all the Andre´ planes as well as all the regular nearfield planes. We discuss Foulser’s λ-planes in Chapter 17 below. The λ-planes, like all Andre´ and nearfield planes, are disjoint from the class of non-Desarguesian planes.
