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.
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Zielgruppe
Für höhere Schule und Studium
Research
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Maße
Höhe: 244 mm
Breite: 170 mm
Dicke: 11 mm
Gewicht
ISBN-13
978-3-7643-8507-1 (9783764385071)
DOI
10.1007/978-3-7643-8508-8
Schweitzer Klassifikation
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.