http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
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.
Chapter 1 An Overview -- chapter 2 Andre's Theory of Spreads -- 2.1 Introduction -- chapter 3 Spreads in PG(3,K) -- 3.1 Introduction -- chapter 4 Partial Spreads and Translation Nets -- 4.1 Introduction -- chapter 5 Spreadsets and Partial Spreadsets -- 5.1 Introduction -- chapter 6 Geometry of Spreadsets: V(r) -- 6.1 Introduction -- chapter 7 Coordinatization by Spreadsets: General Cases -- 7.1 Introduction -- chapter 8 Partial Quasifields -- 8.1 Introduction -- chapter 9 Coordinatization by (Partial) Quasifields -- 9.1 Introduction -- chapter 10 Rational Desarguesian Nets -- 10.1 Introduction -- chapter 11 Quasigroups, Loops and Nuclei -- 11.1 Introduction -- chapter 12 (Pre)Quasifields: Algebraic Axioms and Autotopisms -- 12.1 Introduction -- chapter 13 The Kernel of Spreadsets and Quasifields -- 13.1 Introduction Hom(y, +)that leaves invariant every component. By the Andre theory -- chapter 14 Quadratics of Two-Dimensional Quasifields: Hall Systems -- 14.1 Introduction -- chapter 15 Spreads in Projective Spaces -- 15.1 Introduction -- chapter 16 Kernel Subplanes across Desarguesian Nets -- 16.1 Introduction -- chapter 17 Derivation of Finite Spreads -- 17.1 Introduction -- chapter 18 Foulser's Covering Theorem -- 18.1 Introduction -- chapter 19 Structure of Baer Groups -- 19.1 Introduction -- chapter 20 Frobenius Complements, p-Primitive Collineations, and Klein Groups -- chapter 21 Large Planar Groups -- 21.1 Introduction -- chapter 22 Finite Generalized Andre Systems and Nearfields -- 22.1 Introduction -- chapter 23 Elation Net Theory -- 23.1 Algebra Generated by a Matrix A -- chapter 24 Baer-Elation Theory -- 24.1 Introduction -- chapter 25 Semifields -- 25.1 Introduction -- chapter 26 Simple T-Extensions of Derivable Nets -- 26.1 Introduction -- chapter 27 Cyclic Semifields -- 27.1 Intro duction -- chapter 28 Baer Groups on Parabolic Spreads -- 28.1 Introduction -- chapter 29 Lifting and Quasifibrations -- 29.1 Introduction -- chapter 30 Mixed Tangentially Transitive Planes -- 30.1 Introduction -- chapter 31 Maximal Partial Spreads -- 31.1 Introduction -- chapter 32 Foulser-Johnson SL(2, g)-Theorem -- SL(2, 32,1 Introduction.
by Mauro Biliotti, Vikram Jha and Norman Johnson.
Includes bibliographical references and index.
Monographs and textbooks in pure and applied mathematics