Frontiers in Mathematics

Cardinali, Ilaria; Payne, Stanley E.

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.

Details

Published by: Birkhäuser

Publication Date: 2007-08-16

Format: Paperback

ISBN-13: 9783764385071

DOI: 10.1007/978-3-7643-8508-8

Dimensions: 240cm x170cm

Pages: 166