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q-Clan Geometries in Characteristic 2
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q-Clan Geometries in Characteristic 2 Paperback - 2007

by Ilaria Cardinali; Stanley E. Payne


From the publisher

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.

From the rear cover

This monograph offers the only comprehensive, coherent treatment of the theory - in characteristic 2 - of the so-called flock quadrangles, i.e., those generalized quadrangles (GQ) that arise from q-clans, along with their associated ovals. Special attention is given to the determination of the complete oval stabilizers of each of the ovals associated with a flock GQ. A concise but logically complete introduction to the basic ideas is given. The theory of these flock GQ has evolved over the past two decades and has reached a level of maturation that makes it possible for the first time to give a satisfactory, unified treatment of all the known examples.

The book will be a useful resource for all researchers working in the field of finite geometry, especially those interested in finite generalized quadrangles. It is of particular interest to those studying ovals in finite Desarguesian planes.

Details

  • Title q-Clan Geometries in Characteristic 2
  • Author Ilaria Cardinali; Stanley E. Payne
  • Binding Paperback
  • Edition 1ed
  • Pages 166
  • Volumes 1
  • Language ENG
  • Publisher Birkhauser, Basel
  • Date 2007-10
  • Illustrated Yes
  • ISBN 9783764385071 / 3764385073
  • Weight 0.8 lbs (0.36 kg)
  • Dimensions 6.6 x 9.3 x 0.4 in (16.76 x 23.62 x 1.02 cm)
  • Library of Congress Catalog Number 2007929014
  • Dewey Decimal Code 516.13
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q-Clan Geometries in Characteristic 2
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q-Clan Geometries in Characteristic 2 (Frontiers in Mathematics) (No. 2)
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Q-CLAN GEOMETRIES IN CHARACTERISTIC 2
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