Translation planes of order q<sup>2</sup> admitting collineation groups of order q<sup>3</sup>u preserving a parabolic unital


The set of translation planes of order q<sup>2</sup> that admit collineation groups of order q<sup>3</sup>u, where u is a prime p-primitive divisor of q<sup>2</sup>-1, consists of exactly the Desarguesian plane, assuming that the group does not contain a translation subgroup of order a multiple of q<sup>2</sup>. This applies to show that if the group preserves a parabolic unital then the plane is forced to be Desarguesian.

DOI Code: 10.1285/i15900932v26n2p105

Keywords: Spread; Translation plane; Parabolic unital; Unital group

Classification: 51E23; 51A40

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