Handbook of Finite Translation Planes
Handbook of Finite Translation Planes
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Author(s): Jha, Vikram
Johnson, Norman
ISBN No.: 9781420011142
Pages: 888
Year: 200702
Format: E-Book
E-Book Format Price
DRM PDF $ 149.21

Preface and Acknowledgments. An Overview. Translation Plane Structure Theory. Partial Spreads and Translation Nets. Partial Spreads and Generalizations. Quasifields. Derivation. Frequently Used Tools.


Sharply Transitive Sets. SL(2, p) SL(2, p)-Planes. Classical Semifields. Groups of Generalized Twisted Field Planes. Nuclear Fusion in Semifields. Cyclic Semifields. T-Cyclic GL(2, q)-Spreads. Cone Representation Theory.


Andre Net Replacements and Ostrom-Wilke Generalizations. Foulser's ?-Planes. Regulus Lifts, Intersections over Extension Fields. Hyper-Reguli Arising from Andre Hyper-Reguli. Translation Planes with Large Homology Groups. Derived Generalized Andre Planes. The Classes of Generalized Andre Planes. C-System Nearfields.


Subregular Spreads. Fano Configurations. Fano Configurations in Generalized Andre Planes. Planes with Many Elation Axes. Klein Quadric. Parallelisms. Transitive Parallelisms. Ovoids.


Known Ovoids. Simple T-Extensions of Derivable Nets. Baer Groups on Parabolic Spreads. Algebraic Lifting. Semifield Planes of Orders q4, q6. Known Classes of Semifields. Methods of Oyama-Suetake Planes. Coupled Planes.


Hyper-Reguli. Subgeometry Partitions. Groups on Multiple Hyper-Reguli. Hyper-Reguli of Dimension 3. Elation-Baer Incompatibility. Hering-Ostrom Elation Theorem. Baer-Elation Theory. Spreads Admitting Unimodular Sections-Foulser-Johnson Theorem.


Spreads of Order q2-Groups of Order q2. Transversal Extensions. Indicator Sets. Geometries and Partitions. Maximal Partial Spreads. Sperner Spaces. Conical Flocks. Ostrom and Flock Derivation.


Transitive Skeletons. BLT-Set Examples. Many Ostrom-Derivates. Infinite Classes of Flocks. Sporadic Flocks. Hyperbolic Fibrations. Spreads with Many Homologies. Nests of Reguli.


Chains. Multiple Nests. A Few Remarks on Isomorphisms. Flag-Transitive Geometries. Quartic Groups in Translation Planes. Double Transitivity. Triangle Transitive Planes. Hiramine-Johnson-Draayer Theory.


Bol Planes. 2/3-Transitive Axial.


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