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Flag-transitive extensions of \(C_ n\) geometries. (English) Zbl 0722.51007
A \(c.C_ n\)-geometry is a Buekenhout-Tits geometry belonging to the diagram \(C_ n\) extended by a c-stroke at the opposite side of the double stroke. The paper under review classifies such finite geometries \(\Gamma\) with the following three additional hypotheses; (1) Aut(\(\Gamma\)) acts flat transitively (2) the generalized quadrangle belonging to the double stroke in the diagram are also thick. When (2) is not satisfied, partial results in the literature towards a classification are mentioned. The main result is: under the conditions above, \(\Gamma\) is either an affine polar space of order 2 or a standard quotient, or \(\Gamma\) is one of eight well known sporadic examples.

51E24 Buildings and the geometry of diagrams
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