Vol. 9, No. 1, 2009

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Finite BN-pairs of rank 2, I

Koen Thas

Vol. 9 (2009), No. 1, 189–202
DOI: 10.2140/iig.2009.9.189
Abstract

One of the fundamental problems in Incidence Geometry is the classification of finite BN-pairs of rank 2 (most notably those of type B2), 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 2 (and the buildings that arise) for which the associated parameters (s,t) are powers of 2, 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 (s,t) with st a power of 2, admitting a BN-pair. (For quadrangles and hexagons, this result will be obtained in part II.)

Keywords
BN-pair, generalized polygon, classification
Mathematical Subject Classification 2000
Primary: 20B25, 20E42, 51E12
Milestones
Received: 11 June 2007
Accepted: 10 October 2009
Authors
Koen Thas
University of Ghent
Belgium