Abstract
If Γ is a half-Moufang generalized hexagon, then Γ is Moufang. We also give a very short proof that a generalized hexagon admitting a split BN-pair is a Moufang hexagon.
Similar content being viewed by others
References
J. D. Dixon and B. Mortimer,Permutation Groups, Graduate Texts in Mathematics163, Springer, Berlin, 1996.
P. Fong and G. Seitz,Groups with a (B, N)-pair of rank 2.I, II, Inventiones Mathematicae21 (1973), 1–57;24 (1974), 191–239.
S. Payne, J. A. Thas and H. Van Maldeghem,Half Moufang implies Moufang for finite generalized quadrangles, Inventiones Mathematicae105 (1991), 153–156.
M. A. Ronan,A geometric characterization of Moufang hexagons, Inventiones Mathematicae57 (1980), 227–262.
K. Tent,Split BN-pairs of finite Morley Rank, Annals of Pure and Applied Logic119 (2003), 239–264.
K. Tent,(B,N)-pairs of rank 2: the octagons, Advances in Mathematics181 (2004), 308–320.
K. Tent,Half-Moufang implies Moufang for generalized quadrangles, Journal für die reine und angewandte Mathematik, to appear.
K. Tent and H. Van Maldeghem,On irreducible split (B,N)-pairs of rank 2, Forum Mathematicum13 (2001), 853–862.
K. Tent and H. Van Maldeghem,Moufang polygons and irreducible spherical BN-pairs of rank 2, I, Advances in Mathematics174 (2003), 254–265.
J. Tits,Sur la trialité et certain groupes qui s’en déduisent, Publications Mathématiques de l’Institut des Hautes Études Scientifiques2 (1959), 13–60.
J. Tits and R. Weiss,Moufang Polygons, Monographs in Mathematics, Springer, Berlin, 2002.
H. Van Maldeghem,Generalized Polygons, Birkhäuser, Basel, 1998.
Author information
Authors and Affiliations
Corresponding author
Additional information
Supported by a Heisenberg-Stipendium.
Rights and permissions
About this article
Cite this article
Tent, K. Half-moufang generalized hexagons. Isr. J. Math. 141, 83–92 (2004). https://doi.org/10.1007/BF02772212
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02772212