Generalized Quadrangles with an Abelian Singer Group
نویسندگان
چکیده
In this note we characterize thick finite generalized quadrangles constructed from a generalized hyperoval as those admitting an abelian Singer group, i.e., an abelian group acting regularly on the points.
منابع مشابه
Generalized Quadrangles and Transitive Pseudo-Hyperovals
A pseudo-hyperoval of a projective space PG(3n− 1, q), q even, is a set of q +2 subspaces of dimension n − 1 such that any three span the whole space. We prove that a pseudo-hyperoval with an irreducible transitive stabiliser is elementary. We then deduce from this result a classification of the thick generalised quadrangles Q that admit a point-primitive, line-transitive automorphism group wit...
متن کاملLocal Sharply Transitive Actions on Finite Generalized Quadrangles
We classify the finite generalized quadrangles containing a line L such that some group of collineations acts sharply transitively on the ordered pentagons which start with two points of L. This can be seen as a generalization of a result of Thas and the second author [22] classifying all finite generalized quadrangles admitting a collineation group that acts transitively on all ordered pentago...
متن کاملSome Generalized Quadrangles with Parameters q 2 , q
To Professor Helmut Wielandt, to commemorate his seventy-fifth birthday 1. Introduction In [2] a new generalized quadrangle with parameters q2, q was constructed using the G 2(q) generalized hexagon (q == 2 (mod 3), q > 2). In addition, an elementary group theoretic technique was presented for constructing generalized quadrangles. This technique was refined by Payne [3] in order to simplify cal...
متن کاملOn Finite Elation Generalized Quadrangles with Symmetries
We study the structure of finite groups G which act as elation groups on finite generalized quadrangles and contain a full group of symmetries about some line through the base point. Such groups are related to the translation groups of translation transversal designs with parameters depending on those of the quadrangles. Using results on the structure of /^-groups which act as translation group...
متن کاملMoufang-like conditions for generalized quadrangles and classification of all finite quasi-transitive generalized quadrangles
We tell the history ofMoufang generalized quadrangles.We review someMoufang-like conditions, and classify finite quasi-transitive generalized quadrangles. These are generalized quadrangles so that for any two non-concurrent linesU,V of theGQ, and for someW ∈ {U,V }⊥, the group of generalized homologies with axes U and V acts transitively on the points ofW incident with neither U nor V. As a by-...
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:
- Des. Codes Cryptography
دوره 39 شماره
صفحات -
تاریخ انتشار 2006