On Generalized Hexagons and a Near Octagon whose Lines have Three Points

On Generalized Hexagons and a Near Octagon whose Lines have Three Points

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On Near Hexagons and Spreads of Generalized Quadrangles

The glueing-construction described in this paper makes use of two generalized quadrangles with a spread in each of them and yields a partial linear space with special properties. We study the conditions under which glueing will give a near hexagon. These near hexagons satisfy the nice property that every two points at distance 2 are contained in a quad. We characterize the class of the “glued n...

Coordinatization structures for generalized quadrangles and glued near hexagons

A generalized admissible triple is a triple T = (L, X,∆), where X is a set of size s + 1 ≥ 2, L is a Steiner system S(2, s + 1, st + 1), t ≥ 1, with point-set P and ∆ is a very nice map from P × P to the group Sym(X) of all permutations of the set X. Generalized admissible triples can be used to coordinatize generalized quadrangles with a regular spread and glued near hexagons. The idea of coor...

Integral Points on Quadrics in Three Variables Whose Coordinates Have Few Prime Factors

Non-abelian representations of the slim dense near hexagons on 81 and 243 points

We prove that the near hexagon Q(5,2)× L3 has a non-abelian representation in the extra-special 2-group 21+12 + and that the near hexagon Q(5,2)⊗Q(5,2) has a non-abelian representation in the extra-special 2-group 21+18 − . The description of the non-abelian representation of Q(5,2)⊗Q(5,2) makes use of a new combinatorial construction of this near hexagon.