A parabolic unital U of a translation plane is called transitive, if the collineation group G fixing U fixes the point at infinity of U and acts transitively on the affine points of U. It has been conjectured that if a transitive parabolic unital U consists of the absolute points of a unitary polarity in a commutative semi-field plane, then the sharply transitive normal subgroupK of G is not commutative. So far, this has been proved for commutative twisted field planes of odd square order, see ,. Here we prove this conjecture for commutative Dickson planes.
|Titolo:||Polarity and transitive parabolic unitals in translation planes of odd order|
|Data di pubblicazione:||2002|
|Digital Object Identifier (DOI):||10.1007/PL00012528|
|Appare nelle tipologie:||1.1 Articolo in rivista|