Abstract
The research in this paper was motivated by one of the most important open problems in the theory of generalized polygons, namely the existence problem for semi–finite thick generalized polygons. We show here that no semi–finite generalized hexagon of order (2, t) can have a subhexagon H of order 2. Such a subhexagon is necessarily isomorphic to the split Cayley generalized hexagon H(2) or its point–line dual H D(2). In fact, the employed techniques allow us to prove a stronger result. We show that every near hexagon \({\mathcal{S}}\) of order (2, t) which contains a generalized hexagon H of order 2 as an isometrically embedded subgeometry must be finite. Moreover, if \({H \cong H^{D}}\)(2) then \({\mathcal{S}}\) must also be a generalized hexagon, and consequently isomorphic to either H D(2) or the dual twisted triality hexagon T(2, 8).
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05 June 2019
In the paper mentioned in the title, we showed that there does not exist any infinite near hexagon of order (2,��t) that contains an isometrically embedded subgeometry isomorphic to H(2). The proof of this result contained an error which we correct here.
05 June 2019
In the paper mentioned in the title, we showed that there does not exist any infinite near hexagon of order (2,��t) that contains an isometrically embedded subgeometry isomorphic to H(2). The proof of this result contained an error which we correct here.
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Bishnoi, A., De Bruyn, B. On Semi-Finite Hexagons of Order (2, t) Containing a Subhexagon. Ann. Comb. 20, 433–452 (2016). https://doi.org/10.1007/s00026-016-0315-z
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DOI: https://doi.org/10.1007/s00026-016-0315-z