Polarities of shift planes

Norbert Knarr & Markus Stroppel
We construct polarities for arbitrary shift planes and develop criteria for conjugacy under the normalizer of the shift group. Under suitable assumptions (in particular, for finite or compact planes) we construct all shift groups on a given plane, and our constructions yield all conjugacy classes of polarities. We show that a translation plane admits an orthogonal polarity if, and only if, it is a shift plane. The corresponding planes are exactly those that can be...
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