q-Clan Geometries in Characteristic 2

By Stanley E. Payne and Ilaria Cardinali

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.

• Format: Paperback
• Language: English
• ISBN: 3764385073
• ISBN13: 9783764385071
• Release Date: August 2007
• Publisher: Birkhauser
• Length: 166 Pages
• Weight: 0.80 lbs.
• Dimensions: 0.4" x 9.3" x 6.6"