Foundations of Translation Planes

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CRC Press, Jul 13, 2001 - Mathematics - 558 pages
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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.
 

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Contents

An Overview
1
Andres Theory of Spreads
9
Spreads in PG3 K
25
Partial Spreads and Translation Nets
39
Spreadsets and Partial Spreadsets
59
Vr
69
General Cases
95
Partial Quasifields
119
Structure of Baer Groups
283
Frobenius Complements pPrimitive Collineations and Klein
297
Large Planar Groups
305
Finite Generalized Andre Systems and Nearfields
317
Elation Net Theory
339
BaerElation Theory
361
Semifields
383
Simple TExtensions of Derivable Nets
401

Coordinatization by Partial Quasifields
135
Rational Desarguesian Nets
155
Quasigroups Loops and Nuclei
163
Algebraic Axioms and Autotopisms
175
The Kernel of Spreadsets and Quasifields
215
Hall Systems
229
Spreads in Projective Spaces
243
Kernel Subplanes across Desarguesian Nets
255
Derivation of Finite Spreads
263
Foulsers Covering Theorem
275
Cyclic Semifields
415
Baer Groups on Parabolic Spreads
421
Lifting and Quasifibrations
437
Mixed Tangentially Transitive Planes
467
Maximal Partial Spreads
481
FoulserJohnson SL2 gTheorem
489
APPENDICES
499
BIBLIOGRAPHY
527
INDEX
535
Copyright

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Page 528 - Subplanes of partial spreads in translation planes. Bull. London Math. Soc.
Page 529 - Johnson, NL, The translation planes of order q2 that admit SL(2,q) as a collineation group I. Even Order, J. Algebra 86 (1984), 385-406.

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