Moufang-like conditions for generalized quadrangles and classification of all finite quasi-transitive generalized quadrangles

@article{Thas2005MoufanglikeCF,
  title={Moufang-like conditions for generalized quadrangles and classification of all finite quasi-transitive generalized quadrangles},
  author={Koen Thas and Hendrik Van Maldeghem},
  journal={Discrete Mathematics},
  year={2005},
  volume={294},
  pages={203-217}
}
We tell the history of Moufang generalized quadrangles.We review someMoufang-like conditions, and classify finitequasi-transitivegeneralized quadrangles. These are generalized quadrangles so that for any twonon-concurrent lines U,V of theGQ,and for some W ∈ {U,V }⊥, thegroupof generalized homologies with axes U andV acts transitively on the points of W incident with neitherU norV. As a by-product of the proof, we will show, without the classification of finite simple groups, that a finite… CONTINUE READING

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