Unitals in PG(2, q2) with a large 2-point stabiliser
نویسندگان
چکیده
Let U be a unital embedded in the Desarguesian projective plane PG(2, q 2). Write M for the subgroup of PGL(3, q 2) which preserves U. We show that U is classical if and only if U has two distinct points P, Q for which the stabiliser G = MP,Q has order q 2 − 1.
منابع مشابه
Unitals in Finite Desarguesian Planes
We show that a suitable 2-dimensional linear system of Hermitian curves of PG(2, q2) defines a model for the Desarguesian plane PG(2, q). Using this model we give the following group-theoretic characterization of the classical unitals. A unital in PG(2, q2) is classical if and only if it is fixed by a linear collineation group of order 6(q + 1)2 that fixes no point or line in PG(2, q2).
متن کاملIntersections of Nonclassical Unitals and Conics in PG(2,q2)
In PG(2, q2) with q > 2, we determine the possible intersections of a nonclassical Buekenhout–Metz unital U and a conic passing through the point at infinity of U .
متن کاملAn alternative construction of B-M and B-T unitals in desarguesian planes
We present a new construction of non-classical unitals from a classical unital U in PG(2, q2). The resulting non-classical unitals are B-M unitals. The idea is to find a non-standard model Π of PG(2, q2) with the following three properties: (i) points of Π are those of PG(2, q2); (ii) lines of Π are certain lines and conics of PG(2, q2); (iii) the points in U form a non-classical B-M unital in ...
متن کاملConstructions of unitals in Desarguesian planes
We present a new construction of non-classical unitals from a classical unital U in PG(2, q2). The resulting non-classical unitals are B–M unitals. The idea is to find a non-standard model Π of PG(2, q2) with the following three properties: (i) points of Π are those of PG(2, q2); (ii) lines of Π are certain lines and conics of PG(2, q2); (iii) the points in U form a non-classical B–M unital in ...
متن کاملA class of Buekenhout unitals in the Hall plane
Let U be the classical unital in PG(2, q2) secant to `∞. By deriving PG(2, q) with respect to a derivation set disjoint from U we obtain a new unital U ′ in the Hall plane of order q2. We show that this unital contains O’Nan configurations and is not isomorphic to the known unitals of the Hall plane, hence it forms a new class of unitals in the Hall plane.
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:
- Discrete Mathematics
دوره 312 شماره
صفحات -
تاریخ انتشار 2012