Subplane Covered Nets: 1st Edition (Hardback) book cover

Subplane Covered Nets

1st Edition

By Norman L. Johnson

CRC Press

388 pages

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Hardback: 9780824790080
pub: 2000-01-03
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Description

This work confronts the question of geometric processes of derivation, specifically the derivation of affine planes - keying in on construction techniques and types of transformations in which lines of a newly-created plane can be understood as subplanes of the original plane. The book provides a theory of subplane covered nets without restriction to the finite case or imposing commutativity conditions.

Table of Contents

A brief overview; projective geometries; beginning derivation; spreads; derivable nets; the Hughes planes; Desarguesian planes; Pappian planes; characterizations of geometries; derivable nets and geometries; structure theory for derivable nets; dual spreads and Baer subplanes; derivation as a geometric process; embedding; classification of subplane covered nets; subplane covered affine planes; direct products; parallelisms; partial parallelisms with deficiency; Baer extensions; translation planes admitting Baer groups; spreads covered by pseudo-Reguli; conical and ruled planes over fields; spreads which are dual spreads; partial flocks of deficiency one; Skew-Hall planes.

About the Series

Chapman & Hall/CRC Pure and Applied Mathematics

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Subject Categories

BISAC Subject Codes/Headings:
MAT003000
MATHEMATICS / Applied