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

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• 作者：Thas ; Koen ; Van Maldeghem ; Hendrik
• 关键词：05B25 ; 05E20 ; 20B25 ; 20B27 ; 20E42 ; 51E12 ; Moufang quadrangle ; k-Moufang generalized quadrangle ; Elation generalized quadrangle ; Quasi-transitive generalized quadrangle
• 刊名：Discrete Mathematics
• 出版年：2005
• 出版时间：April 28, 2005
• 年：2005
• 卷：294
• 期：1-2
• 页码：203-217
• 全文大小：238 K

文摘

We tell the history of Moufang generalized quadrangles. We review some Moufang-like conditions, and classify finite quasi-transitive generalized quadrangles. These are generalized quadrangles so that for any two non-concurrent lines U,V of the GQ, and for some W{U,V}, the group of generalized homologies with axes U and V acts transitively on the points of W incident with neither U nor V.

As a by-product of the proof, we will show, without the classification of finite simple groups, that a finite generalized quadrangle that admits a BN-pair of rank 2 is classical or dual classical if and only if it admits at least one nontrivial homology (!).