q-Clan Geometries in Characteristic 2

A q-clan with q a power of 2 is equivalent to a certain generalized quadrangle with a family of subquadrangles each associated with an oval in the Desarguesian plane of order 2. It is also equivalent to a flock of a quadratic cone, and hence to a line-spread of 3-dimensional projective space and thus to a translation plane, and more. These geometric objects are tied together by the so-called Fundamental Theorem of q-Clan Geometry. The book gives a complete proof of this theorem, followed by a detailed study of the known examples. The collineation groups of the associated generalized quadrangles and the stabilizers of their associated ovals are worked out completely.

List of contents

q-Clans and Their Geometries.- The Fundamental Theorem.- Aut(GQ(C)).- The Cyclic q-Clans.- Applications to the Known Cyclic q-Clans.- The Subiaco Oval Stabilizers.- The Adelaide Oval Stabilizers.- The Payne q-Clans.- Other Good Stuff.

Summary

A q-clan with q a power of 2 is equivalent to a certain generalized quadrangle with a family of subquadrangles each associated with an oval in the Desarguesian plane of order 2. It is also equivalent to a flock of a quadratic cone, and hence to a line-spread of 3-dimensional projective space and thus to a translation plane, and more. These geometric objects are tied together by the so-called Fundamental Theorem of q-Clan Geometry. The book gives a complete proof of this theorem, followed by a detailed study of the known examples. The collineation groups of the associated generalized quadrangles and the stabilizers of their associated ovals are worked out completely.

Product details

• Authors: Ilari Cardinali, Ilaria Cardinali, Stanley E Payne, Stanley E. Payne
• Publisher: Springer, Basel
• Languages: English
• Product format: Paperback / Softback
• Released: 04.04.2008
• EAN: 9783764385071
• ISBN: 978-3-7643-8507-1
• No. of pages: 166
• Weight: 368 g
• Illustrations: XIV, 166 p.
• Series: Frontiers in Mathematics; Frontiers in Mathematics
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Geometry; B, Diskrete Mathematik, geometry, Theorem, Mathematics and Statistics, Discrete Mathematics, Discrete geometry, Convex and Discrete Geometry, Convex geometry, Object, Proof, quadrangle, fundamental theorem