Subplane Covered Nets

by Norman L. Johnson

Overview

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

Product Details

ISBN-13:	9781040219140
Publisher:	CRC Press
Publication date:	01/03/2000
Series:	Chapman & Hall/CRC Pure and Applied Mathematics
Sold by:	Barnes & Noble
Format:	eBook
Pages:	388
File size:	834 KB

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.

Editorial Reviews

Confronting the question of geometric processes of derivation, Johnson (mathematics, U. of Iowa-Iowa City) specifically addresses the derivation of affine planes, focusing on construction techniques and types of transformations in which lines of a newly created plane can be understood as subplanes of the original plane. Among the aspects he deals with are three-dimensional projective spaces, point-line transitivities, pseudo-regulus nets, four-dimensional vector spaces associated with three-dimensional projective spaces and Abelian transvection groups, derivable nets embedded in projective spaces and corresponding net structures, several types of planes and subplanes, and nets embedded in affine space. He also considers mechanisms such as projective spaces, hyperplanes, parallelism, isomorphism, semilinear groups, and skew-fields. His treatment should be accessible to mathematicians, topologists, combinatorialists, and graduate or upper-level undergraduate students in those fields. Annotation c. Book News, Inc., Portland, OR (booknews.com)

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