On Semi-Finite Hexagons of Order (2, t) Containing a Subhexagon

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• 作者：Anurag Bishnoi ; Bart De Bruyn
• 刊名：Annals of Combinatorics
• 出版年：2016
• 出版时间：September 2016
• 年：2016
• 卷：20
• 期：3
• 页码：433-452
• 全文大小：923 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Combinatorics
  
• 出版者：Birkh盲user Basel
• ISSN：0219-3094
• 卷排序：20

文摘

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 HD(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 HD(2) or the dual twisted triality hexagon T(2, 8).Keywordsgeneralized hexagonnear hexagonvaluation