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Near Polygons Having a big sub Near Polygon Isomorphic to
Bart De Bruyn
Department of Pure Mathematics and Computer Algebra, Ghent University, Galglaan 2, B-9000 Gent, Belgium
Annals of Combinatorics 6 (3) p.285-294 September, 2002
AMS Subject Classification: 05B25, 51E12, 51E25
In [1] a near 2n-gon ,, was constructed from the set of 2-factors of the complete graph on 2n+2 vertices. In this paper, we determine all near 2n-gons, , having as a big geodetically closed sub near 2(n-1)-gon under the additional assumption that every two points at distance 2 have at least two common neighbours. We will prove that such a near 2n-gon is either isomorphic to or to a direct product of with a line. As a corollary of that, the near polygon is characterized by means of the local space at one point.
Keywords: near polygon, generalized quadrangle


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