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.

Table des matières

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)

A propos de l'auteur

Mauro Biliotti, Vikram Jha, Norman Johnson

Résumé

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.

Détails du produit

• Auteurs: 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
• Collaboration: Zuhair Nashed (Editeur de la série), Earl Taft (Editeur de la série)
• Edition: Taylor and Francis
• Langues: Anglais
• Format d'édition: Livre Relié
• Sortie: 13.07.2001
• EAN: 9780824706098
• ISBN: 978-0-8247-0609-8
• Pages: 566
• Poids: 816 g
• Thèmes: Chapman & Hall/CRC Pure and Applied Mathematics; Chapman & Hall/CRC Pure and Applied Mathematics
• Catégories: Sciences naturelles, médecine, informatique, technique > Mathématiques > Géométrie; MATHEMATICS / Geometry / General, MATHEMATICS / Topology, geometry, Topology