The flag-transitive tilde and Petersen-type geometries are all known

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The Flag-transitive Tilde and Petersen-type Geometries Are All Known

We announce the classification of two related classes of flag-transitive geometries. There is an infinite family of such geometries, related to the nonsplit extensions 3 n 2 ] 2 ·Sp2n(2), and twelve sporadic examples coming from the simple groups M22, M23, M24, He, Co1, Co2, J4, BM , M and the nonsplit extensions 3 · M22, 323 · Co2, and 34371 · BM .

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A nite C 3-geometry is called anomalous if it is neither a building nor the A 7-geometry. It is conjectured that no ag-transitive thick anomalous C 3-geometry exists. For a ag-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 ag-transitive circular extensions of duals of anomalous C 3-ge...

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ژورنال

عنوان ژورنال: Bulletin of the American Mathematical Society

سال: 1994

ISSN: 0273-0979

DOI: 10.1090/s0273-0979-1994-00511-7