ABSTRACT
In this chapter, we demonstrate the high degree of incompatibility between Baer p-elements and affine elations, acting on a translation plane π of order p2r. Among the most startling of such results is Foulser’s theorem, asserting that non-trivial Baer p-elements and non-trivial affine elations cannot simul taneously act on π if p is odd. The first section of this chapter establishes striking constraints of this type, all due to Foulser, that apply to transla tion planes of odd order. The second section, due to Jha and Johnson, is concerned with the even order versions of an analogous theory: here affine elations and Baer 2-elements are compatible, but they constrain each other quite severely.
