Beitraege zur Algebra und Geometrie
Contributions to Algebra and Geometry
Volume 34 (1993), No. 2, 277-286.
On Flag-Transitive Anomalous $C_3$-Geometries
Satoshi Yoshiara, Antonio Pasini
Abstract.
A finite $C_{3}$-geometry is called anomalous if it is neither a building nor
the $A_{7}$-geometry. It is conjectured that no flag-transitive thick
anomalous $C_{3}$-geometry exists.
For a flag-transitive thick anomalous $C_{3}$-geometry, we prove that
its $2$-order $y$ is odd and that its full automorphism group is
non-solvable. As a corollary, there are no flag-transitive circular
extensions of duals of anomalous $C_{3}$-geometries.