Handbook of Finite Translation Planes

Norman Johnson, Vikram Jha, Mauro Biliotti

February 15, 2007 by Chapman and Hall/CRC
Reference - 888 Pages
ISBN 9781584886051 - CAT# C6056
Series: Chapman & Hall/CRC Pure and Applied Mathematics


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  • Provides a complete description of all known finite translation planes
  • Includes examples of translation planes and related geometries
  • Connects translation planes with numerous areas of incidence geometry such as flocks of quadric sets, generalized quadrangles, and partitions
  • Supplies all of the varied construction techniques of translation planes
  • Shows the importance of various classes of translation planes by illustrating their place within certain fundamental classification schemes
  • Summary

    The Handbook of Finite Translation Planes provides a comprehensive listing of all translation planes derived from a fundamental construction technique, an explanation of the classes of translation planes using both descriptions and construction methods, and thorough sketches of the major relevant theorems.

    From the methods of André to coordinate and linear algebra, the book unifies the numerous diverse approaches for analyzing finite translation planes. It pays particular attention to the processes that are used to study translation planes, including ovoid and Klein quadric projection, multiple derivation, hyper-regulus replacement, subregular lifting, conical distortion, and Hermitian sequences. In addition, the book demonstrates how the collineation group can affect the structure of the plane and what information can be obtained by imposing group theoretic conditions on the plane. The authors also examine semifield and division ring planes and introduce the geometries of two-dimensional translation planes.

    As a compendium of examples, processes, construction techniques, and models, the Handbook of Finite Translation Planes equips readers with precise information for finding a particular plane. It presents the classification results for translation planes and the general outlines of their proofs, offers a full review of all recognized construction techniques for translation planes, and illustrates known examples.