Foundations of Translation Planes

1. Auflage 2001
ISBN: 978-0-8247-0609-8
Verlag: CRC Press

Buch, Englisch, 566 Seiten, Format (B × H): 216 mm x 279 mm, Gewicht: 816 g

Reihe: Chapman & Hall/CRC Pure and Applied Mathematics

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.

Autoren/Hrsg.

Biliotti, Mauro

Jha, Vikram

Johnson, Norman

Fachgebiete

• Mathematik | Informatik Mathematik Topologie Mengentheoretische Topologie
• Mathematik | Informatik Mathematik Geometrie

Inhaltsverzeichnis

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)

Über Autor(innen)

Mauro Biliotti, Vikram Jha, Norman Johnson