The Theorem of Totten for planar spaces

Abstract

It is shown that an irreducible planar space S with v points and π planes such that n3 ≤ v < (n + 1)3 and π ≤ v + n2 + n for some integer n ≥ 4 exists iff n is a prime power and S either can be embedded in P G(3, n), or S is the affine space AG(3, n) with a generalized projective 3-space at infinity. This result is an analogue to the classification of restricted linear spaces by Totten.

Keywords

• projective space
• planar space