Q-Clan Geometries in Characteristic 2

Ilaria Cardinali, Stanley E. Payne3764385073, 978-3-7643-8507-1

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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Table of contents :
41aKfJnqpmL……Page 1
front-matter……Page 2
01q-Clans and Their Geometries……Page 15
02The Fundamental Theorem……Page 32
03Aut(GQ( C ))……Page 59
04The Cyclic q-Clans……Page 85
05Applications to the Known Cyclic q-Clans……Page 103
06The Subiaco Oval Stabilizers……Page 113
07The Adelaide Oval Stabilizers……Page 144
08The Payne q-Clans……Page 151
09Other Good Stuff……Page 159
back-matter……Page 168