Geodesic
On Unitary Polarities of Finite Projective Planes
Canadian journal of mathematics, Tome 23 (1971) no. 6, pp. 1060-1077

Voir la notice de l'article provenant de la source Cambridge University Press

A unitary polarity of a finite projective plane of order q 2 is a polarity θ having q 3 + 1 absolute points and such that each nonabsolute line contains precisely q + 1 absolute points. Let G(θ) be the group of collineations of centralizing θ. In [15] and [16], A. Hoffer considered restrictions on G(θ) which force to be desarguesian. The present paper is a continuation of Hoffer's work. The following are our main results.THEOREM I. Let θ be a unitary polarity of a finite projective planeof order q 2. Suppose that Γ is a subgroup of G(θ) transitive on the pairs x, X, with x an absolute point and X a nonabsolute line containing x. Thenis desarguesian and Γ contains PSU(3, q). 
Kantor, William M. On Unitary Polarities of Finite Projective Planes. Canadian journal of mathematics, Tome 23 (1971) no. 6, pp. 1060-1077. doi: 10.4153/CJM-1971-110-9
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