Details

q-Clan Geometries in Characteristic 2

q-Clan Geometries in Characteristic 2


Frontiers in Mathematics

von: Ilaria Cardinali, Stanley E. Payne

58,84 €

Verlag: Birkhäuser
Format: PDF
Veröffentl.: 03.01.2008
ISBN/EAN: 9783764385088
Sprache: englisch
Anzahl Seiten: 180

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Beschreibungen

Titelbeschreibung

<P>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.&nbsp;The book gives a&nbsp;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.</P>

Inhaltsverzeichnis

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.

Back cover copy

<P>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&nbsp;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. </P>
<P>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&nbsp;particular interest to those studying ovals in finite Desarguesian planes.</P>
<P>&nbsp;</P>

Sonderbeitrag

Includes supplementary material: sn.pub/extras

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