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q-Clan Geometries in Characteristic 2

  • Book
  • © 2007

Overview

Authors:
  1. Ilaria Cardinali

    1. Department of Mathematics, University of Siena, Siena, Italy

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  2. Stanley E. Payne

    1. Department of Mathematical Sciences, University of Colorado at Denver and Health Sciences Center, Denver, USA

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    You can also search for this author in PubMed   Google Scholar

Part of the book series: Frontiers in Mathematics (FM)

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Table of contents (9 chapters)

  1. Front Matter

    Pages i-xiv
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  2. q-Clans and Their Geometries

    Pages 1-17

  3. The Fundamental Theorem

    Pages 19-45

  4. Aut(GQ(C))

    Pages 47-72

  5. The Cyclic q-Clans

    Pages 73-90

  6. Applications to the Known Cyclic q-Clans

    Pages 91-100

  7. The Subiaco Oval Stabilizers

    Pages 101-131

  8. The Adelaide Oval Stabilizers

    Pages 133-139

  9. The Payne q-Clans

    Pages 141-148

  10. Other Good Stuff

    Pages 149-157

  11. Back Matter

    Pages 159-166
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Keywords

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.

Authors and Affiliations

  • Department of Mathematics, University of Siena, Siena, Italy

    Ilaria Cardinali

  • 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

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