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 [1],[5]. Here we prove this conjecture for commutative Dickson planes.

Polarity and transitive parabolic unitals in translation planes of odd order / Abatangelo, Vito; Larato, Bambina. - In: JOURNAL OF GEOMETRY. - ISSN 0047-2468. - STAMPA. - 74:1-2(2002), pp. 1-6. [10.1007/PL00012528]

Polarity and transitive parabolic unitals in translation planes of odd order

Vito Abatangelo;Bambina Larato
2002-01-01

Abstract

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 [1],[5]. Here we prove this conjecture for commutative Dickson planes.
2002
Polarity and transitive parabolic unitals in translation planes of odd order / Abatangelo, Vito; Larato, Bambina. - In: JOURNAL OF GEOMETRY. - ISSN 0047-2468. - STAMPA. - 74:1-2(2002), pp. 1-6. [10.1007/PL00012528]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11589/10432
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