Translation planes of order
admitting collineation groups of order
preserving a parabolic unital
Abstract
The set of translation planes of order
that admit collineation groups of order
, where u is a prime p-primitive divisor of
, consists of exactly the Desarguesian plane, assuming that the group does not contain a translation subgroup of order a multiple of
. This applies to show that if the group preserves a parabolic unital then the plane is forced to be Desarguesian.
![q<sup>2</sup>](http://siba-ese.unile.it/plugins/generic/latexRender/cache/7af7b909046a345a8acb937438fc3421.png)
![q<sup>3</sup>u](http://siba-ese.unile.it/plugins/generic/latexRender/cache/6b55f53b96f024fc5f849c1399583f1f.png)
![q<sup>2</sup>-1](http://siba-ese.unile.it/plugins/generic/latexRender/cache/2e0b22c266e15d9f3bfba76b0ca486d6.png)
![q<sup>2</sup>](http://siba-ese.unile.it/plugins/generic/latexRender/cache/7af7b909046a345a8acb937438fc3421.png)
DOI Code:
10.1285/i15900932v26n2p105
Keywords:
Spread; Translation plane; Parabolic unital; Unital group
Classification:
51E23; 51A40
Full Text: PDF