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.

Sommario

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.

Riassunto

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.

Dettagli sul prodotto

• Autori: Ilari Cardinali, Ilaria Cardinali, Stanley E Payne, Stanley E. Payne
• Editore: Springer, Basel
• Lingue: Inglese
• Formato: Tascabile
• Pubblicazione: 04.04.2008
• EAN: 9783764385071
• ISBN: 978-3-7643-8507-1
• Pagine: 166
• Peso: 368 g
• Illustrazioni: XIV, 166 p.
• Serie: Frontiers in Mathematics; Frontiers in Mathematics
• Categorie: Scienze naturali, medicina, informatica, tecnica > Matematica > Geometria; B, Diskrete Mathematik, geometry, Theorem, Mathematics and Statistics, Discrete Mathematics, Discrete geometry, Convex and Discrete Geometry, Convex geometry, Object, Proof, quadrangle, fundamental theorem