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Includes supplementary material: sn.pub/extras
Part of the book series: Frontiers in Mathematics (FM)
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Table of contents (9 chapters)
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Front Matter
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Back Matter
About this book
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.
Keywords
- Dimension
- automorphism group
- boundary element method
- character
- discrete geometry
- fundamental theorem
- geometry
- object
- proof
- quadrangle
- theorem
Authors and Affiliations
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Department of Mathematics, University of Siena, Siena, Italy
Ilaria Cardinali
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Department of Mathematical Sciences, University of Colorado at Denver and Health Sciences Center, Denver, USA
Stanley E. Payne
Bibliographic Information
Book Title: q-Clan Geometries in Characteristic 2
Authors: Ilaria Cardinali, Stanley E. Payne
Series Title: Frontiers in Mathematics
DOI: https://doi.org/10.1007/978-3-7643-8508-8
Publisher: Birkhäuser Basel
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Birkhäuser Basel 2007
Softcover ISBN: 978-3-7643-8507-1Published: 16 August 2007
eBook ISBN: 978-3-7643-8508-8Published: 03 January 2008
Series ISSN: 1660-8046
Series E-ISSN: 1660-8054
Edition Number: 1
Number of Pages: XIV, 166
Topics: Convex and Discrete Geometry