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.

Zusammenfassung

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.

Produktdetails

• Autoren: Ilaria Cardinali, Stanley E. Payne, Ilari Cardinali, Stanley E Payne
• Verlag: Springer, Basel
• Inhalt: Buch
• Produktform: Taschenbuch
• Erscheinungsdatum: 04.04.2008
• Thema: Naturwissenschaften, Medizin, Informatik, Technik > Mathematik > Geometrie
• EAN: 9783764385071
• ISBN: 978-3-7643-8507-1
• Anzahl Seiten: 166
• Illustration: XIV, 166 p.
• Höhe (Verpackung): 24 cm
• Gewicht (Verpackung): 368 g
• Serie: Frontiers in Mathematics; Frontiers in Mathematics
• Themen: B, Diskrete Mathematik, geometry, Theorem, Mathematics and Statistics, Discrete Mathematics, Discrete geometry, Convex and Discrete Geometry, Convex Geometry, Object, Proof, quadrangle, fundamental theorem