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Journal of the London Mathematical Society 2000 62(1):1-15; doi:10.1112/S0024610700001022
© 2000 by London Mathematical Society
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© The London Mathematical Society

Very Homogeneous Generalized n-Gons of Finite Morley Rank

K. Tent

Mathematisches Institut, Universität Würzburg Am Hubland, 97074 Würzburg, Germany, tent{at}mathematik.uni-wuerzburg.de

Received 23 November 1998. Revision received 9 June 1999.

(Almost strongly minimal) generalized n-gons are constructed for all n ≥ 3 for which the automorphism group acts transitively on the set of ordered ordinary (n + 1)-gons contained in it, a new class of BN-pairs thus being obtained. Through the construction being modified slightly, 2N0 many non-isomorphic almost strongly minimal generalized n-gons are obtained for all n ≥ 3, none of which interprets an infinite group. Furthermore, a characterization is given of all graphs whose simple cycles all have length 2n for some n ≥ 3.


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