Abstract
It is shown that a flag-transitive C 3-geometry of finite order (x, y) with x ≥ 2 is either a finite building of type C 3 (and hence the classical polar space for a 6-dimensional symplectic space, a 6-dimensional orthogonal space of plus type, a 6- or 7-dimensional hermitian space, a 7-dimensional orthogonal space, or an 8-dimensional orthogonal space of minus type) or the sporadic A7-geometry with 7 points.
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Yoshiara, S. The Flag-Transitive C 3-Geometries of Finite Order. Journal of Algebraic Combinatorics 5, 251–284 (1996). https://doi.org/10.1023/A:1022480312547
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DOI: https://doi.org/10.1023/A:1022480312547