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.
Reihe
Sprache
Verlagsort
Verlagsgruppe
Zielgruppe
Für höhere Schule und Studium
Für Beruf und Forschung
Maße
Höhe: 229 mm
Breite: 152 mm
Gewicht
ISBN-13
978-0-8247-0609-8 (9780824706098)
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Schweitzer Klassifikation
Mauro Biliotti, Vikram Jha, Norman Johnson
Autor*in
University Di Leece/Matematica, Leece, Italy
Caledonian University, Glasgow, Scotland
University of Iowa, Iowa City, USA
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)
