Beiträge zur Algebra und Geometrie <BR> Contributions to Algebra and GeometryVol. 40, No. 2, pp. 503-531 (1999)

Flag-transitive Extensions of Dual Affine Spaces

Cecile Huybrechts, Antonio Pasini

Universite Libre de Bruxelles, Departement de Mathematique, Campus Plaine, CP 216, Bd du Triomphe, B-1050 Bruxelles, Belgique

Universita di Siena, Dipartimento di Matematica Via del Capitano 15, 53100 Siena, Italia

Abstract: We construct a simply connected flag-transitive circular extension of the dual affine space $AG^*(3,4)$, with $2^{13}\colon 3^{\textstyle\cdot} M_{22}.2$ as full automorphism group and we show that this geometry as well as its unique flag-transitive proper quotient are the unique flag-transitive circular extensions of finite thick dual affine spaces whose full automorphism group does not induce a 1-dimensional affine group on their point- or plane-residues. Moreover, we observe that our theorem has some nice repercussions for a problem in projective spaces.

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