Extending Polar Spaces of Rank at Least 3
نویسنده
چکیده
It is shown that the extended polar space for the sporadic Fischer group Fi22 is the only extended polar space which has more than two extended planes on a block and is not isomorphic to a quotient of an affine polar space over GF(2). New examples of EGQ(4, 1) and EGQ(4, 2) are presented as well.
منابع مشابه
Point-line characterizations of Lie geometries
There are two basic theorems. Let G be a strong parapolar space with these three properties: (1) For each point x and symplecton S, x is collinear to some point of S. (2) The set of points at distance at most two from a point forms a geometric hyperplane. (3) If every symplecton has rank at least three, every maximal singular subspace has finite projective rank. Then G is either D6; 6;A5; 3 or ...
متن کاملA characterization of finite symplectic polar spaces of odd prime order
A sufficient condition for the representation group for a nonabelian representation (Definition 1.1) of a finite partial linear space to be a finite p-group is given (Theorem 2.9). We characterize finite symplectic polar spaces of rank r at least two and of odd prime order p as the only finite polar spaces of rank at least two and of prime order admitting nonabelian representations. The represe...
متن کاملOn a Class of Hyperplanes of the Symplectic and Hermitian Dual Polar Spaces
Let ∆ be a symplectic dual polar space DW (2n−1, K) or a Hermitian dual polar space DH(2n − 1, K, θ), n ≥ 2. We define a class of hyperplanes of ∆ arising from its Grassmann-embedding and discuss several properties of these hyperplanes. The construction of these hyperplanes allows us to prove that there exists an ovoid of the Hermitian dual polar space DH(2n−1, K, θ) arising from its Grassmann-...
متن کاملLocally subquadrangular hyperplanes in symplectic and Hermitian dual polar spaces
In [11] all locally subquadrangular hyperplanes of finite symplectic and Hermitian dual polar spaces were determined with the aid of counting arguments and divisibility properties of integers. In the present note we extend this classification to the infinite case. We prove that symplectic dual polar spaces and certain Hermitian dual polar spaces cannot have locally subquadrangular hyperplanes i...
متن کاملOn the simple connectedness of hyperplane complements in dual polar spaces
Let ∆ be a dual polar space of rank n ≥ 4, H be a hyperplane of ∆ and Γ := ∆\H be the complement of H in ∆. We shall prove that, if all lines of ∆ have more than 3 points, then Γ is simply connected. Then we show how this theorem can be exploited to prove that certain families of hyperplanes of dual polar spaces, or all hyperplanes of certain dual polar spaces, arise from embeddings.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- J. Comb. Theory, Ser. A
دوره 72 شماره
صفحات -
تاریخ انتشار 1995