Abstract

Abstract We construct polarities for projective planes admitting a group of automorphisms that acts regularly on the complements of an anti-flag in the point and line set. In particular, we determine all polarities of the compact connected planes studied by I. Schellhammer and by P. Sperner. For both classes of planes we solve the conjugacy problem, and determine the set of absolute points for each one of the polarities. Among these polarities we find the first examples of elliptic polarities in non-Moufang compact projective planes.

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