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On flag-transitive anomalous \(C_ 3\)-geometries. (English) Zbl 0802.51011

The authors’ 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”.

MSC:

51E25 Other finite nonlinear geometries
51A10 Homomorphism, automorphism and dualities in linear incidence geometry
05B25 Combinatorial aspects of finite geometries
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