The Valuations of the Near Octagon I4
نویسندگان
چکیده
The maximal and next-to-maximal subspaces of a nonsingular parabolic quadric Q(2n, 2), n ≥ 2, which are not contained in a given hyperbolic quadric Q+(2n − 1, 2) ⊂ Q(2n, 2) define a sub near polygon In of the dual polar space DQ(2n, 2). It is known that every valuation of DQ(2n, 2) induces a valuation of In. In this paper, we classify all valuations of the near octagon I4 and show that they are all induced by a valuation of DQ(8, 2). We use this classification to show that there exists up to isomorphism a unique isometric full embedding of In into each of the dual polar spaces DQ(2n, 2) and DH(2n − 1, 4).
منابع مشابه
A New Near Octagon and the Suzuki Tower
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عنوان ژورنال:
- Electr. J. Comb.
دوره 13 شماره
صفحات -
تاریخ انتشار 2006