## Abstract

Ostrom and Wagner (1959) proved that if the automorphism group G of a finite projective plane π acts 2-transitively on the points of π, then π is isomorphic to the Desarguesian projective plane and G is isomorphic to PΓL(3, q) (for some prime-power q). In the more general case of a finite rank 2 irreducible spherical building, also known as a generalized polygon, the theorem of Fong and Seitz (1973) gave a classification of the Moufang examples. A conjecture of Kantor, made in print in 1991, says that there are only two non-classical examples of flag-transitive generalized quadrangles up to duality. Recently, the authors made progress toward this conjecture by classifying those finite generalized quadrangles which have an automorphism group G acting transitively on antiflags. In this paper, we take this classification much further by weakening the hypothesis to G being transitive on ordered pairs of collinear points and ordered pairs of concurrent lines.

Original language | English |
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Pages (from-to) | 1935-1978 |

Number of pages | 44 |

Journal | Transactions of the American Mathematical Society |

Volume | 374 |

Issue number | 3 |

DOIs | |

Publication status | Published - Mar 2021 |