Abstract
One of the fundamental problems in Incidence Geometry is the classification of finite BN-pairs of rank (most notably those of type ), without the use of the classification theorem for finite simple groups. In this paper, which is the first in a series, we classify finite BN-pairs of rank (and the buildings that arise) for which the associated parameters are powers of , and such that the associated polygon has no proper thick ideal or full subpolygons. As a corollary, we obtain the complete classification of generalized octagons of order with a power of , admitting a BN-pair. (For quadrangles and hexagons, this result will be obtained in part II.)
Citation
Koen Thas. "Finite BN-pairs of rank 2, I." Innov. Incidence Geom. 9 189 - 202, 2009. https://doi.org/10.2140/iig.2009.9.189
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