Abstract
We characterise all spreads that are obtainable from Desarguesian spreads by replacing a partial spread consisting of translation ovals; the corresponding “ovally-derived” planes are generalised Andre planes, of order 2 N , although not all generalised Andre planes are ovallyderived from Desarguesian planes. Our analysis allows us to obtain a complete classification of all nearfield planes that are ovally-derived from Desarguesian planes. It turns out that whether or not a nearfield plane is ovally-derived from a Desarguesian plane depends solely on the parametersq andr, where GF (q) is the kern, andr is the dimension of the plane. Our results also imply that a Hall plane of even orderq2 can be ovally-derived from a Desarguesian spread if and only ifq is a square.
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