Foundations of Translation Planes

An exploration of the construction and analysis of translation planes to spreads, partial spreads, co-ordinate structures, automorphisms, autotopisms, and collineation groups. It emphasizes the manipulation of incidence structures by various co-ordinate systems, including quasisets, spreads and matrix spreadsets. The volume showcases methods of structure theory as well as tools and techniques for the construction of new planes.

List of contents

Andre's theory of spreads; spreads in PG(3,K); partial spreads and translation nets; spreadsheets and partial spreadsets; geometry of spreadsets; co-ordinatization by spreadsets - general cases; partial quasifields; co-ordinatization by (partial) quasifields; rational desarguesian nets; quasigroups, loops and nuclei; (pre)quasifields -algebraic axioms and autopisms; the kernel of spreadsets and quasifields; quadratics of two dimensional quasifields - Hall systems; spreads in projective spaces; kernel subplanes across Desarguesian nets; derivation of finite spreads; Foulser's covering theorem; structure of Baer groups; Frobenius complements, p-primitive collineations, and Klein-4 groups; large planar groups; finite generalized Andre systems and nearfields; elation net theory; Baer-elation theory; semifields. (Part contents)

About the author

Mauro Biliotti, Vikram Jha, Norman Johnson

Summary

An exploration of the construction and analysis of translation planes to spreads, partial spreads, co-ordinate structures, automorphisms, autotopisms, and collineation groups. It emphasizes the manipulation of incidence structures by various co-ordinate systems, including quasisets, spreads and matrix spread sets.

Product details

• Authors: Mauro Biliotti, Mauro (University Di Leece/Matematica Biliotti, Biliotti Mauro, Vikram Jha, Vikram (Caledonian University Jha, Jha Vikram, Norman Johnson, Norman (University of Iowa Johnson, Norman L. Johnson
• Assisted by: Zuhair Nashed (Editor of the series), Earl Taft (Editor of the series)
• Publisher: Taylor and Francis
• Languages: English
• Product format: Hardback
• Released: 13.07.2001
• EAN: 9780824706098
• ISBN: 978-0-8247-0609-8
• No. of pages: 566
• Weight: 816 g
• Series: Chapman & Hall/CRC Pure and Applied Mathematics; Chapman & Hall/CRC Pure and Applied Mathematics
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Geometry; MATHEMATICS / Geometry / General, MATHEMATICS / Topology, geometry, Topology