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