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Johnson M., Jha W., Biliotti M. — Handbook of Finite Translation Planes
Johnson M., Jha W., Biliotti M. — Handbook of Finite Translation Planes



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Название: Handbook of Finite Translation Planes

Авторы: Johnson M., Jha W., Biliotti M.

Аннотация:

The Handbook of Finite Translation Planes provides a comprehensive listing of all translation planes derived from a fundamental construction technique, an explanation of the classes of translation planes using both descriptions and construction methods, and thorough sketches of the major relevant theorems. From the methods of André to coordinate and linear algebra, the book unifies the numerous diverse approaches for analyzing finite translation planes. It pays particular attention to the processes that are used to study translation planes, including ovoid and Klein quadric projection, multiple derivation, hyper-regulus replacement, subregular lifting, conical distortion, and Hermitian sequences. In addition, the book demonstrates how the collineation group can affect the structure of the plane and what information can be obtained by imposing group theoretic conditions on the plane. The authors also examine semifield and division ring planes and introduce the geometries of two-dimensional translation planes. As a compendium of examples, processes, construction techniques, and models, the Handbook of Finite Translation Planes equips readers with precise information for finding a particular plane. It presents the classification results for translation planes and the general outlines of their proofs, offers a full review of all recognized construction techniques for translation planes, and illustrates known


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2007

Количество страниц: 861

Добавлена в каталог: 08.05.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
System of Generators of a Hyperbolic Quadric      779
T -Distortion      253
T -Extension      252
t-base      760
t-design      393
t-Nest of Reguli      472
t-Spread      390
T-Transpose-Extension      252
Tangent to an Oval Cone      339
Thas — Herssens — De Clerck Plane      499
Thas — Walker Construction      397
Thas, Bader — Lunardon Theorem on Hyperbolic Flocks      555
Theorem on Derivation and Projective Space      49
Theorem on Semifields Two Baer Subnuclei      102
Theorems on Coxeter Groups and Lattices      759
Theorems on Quartic Groups      785
Tits Ovoid      245
Totally isotropic      379
Transitive Extensions of Flag-Transitive Planes      543
Transitive Skeletons      443
Transitive Skew Parallelism      369
Translation Dual      619
Translation Net      13 16
Translation Oval      536
Translation Ovoid      619
Translation Ovoid of the Klein Quadric      643
Translation plane      5
Translation Sperner Space      407
Translation Sperner Spread      407
Transpose of a Semifield      620
Transposed Translation Plane      357
Transversal      48 359
Transversal Extension Theory      357
Transversal Function      359
Transversal Spread      358 376
Transversal to a Net      375
Transversal-Free Translation Nets      406
Triangle Transitive Translation Planes      289 516
Triple-Nest      492
Twisted cubic      338
Twisted Fields      72
Unital      393
Unital in PG(3,K)      649
Unitary group      379
Unitary polarity      379
Vector-Space Net      226
Vega Planes of Small Orders      578
Veronesian Variety      563
Wagner’s Theorem      503 790
Walker Planes of Order 25      339
Walker Skeleton      439 798
Walker — Schaeffer Theorem      341
Walker’s Theorem on Subregular Spreads      180
Weakly Coupled Translation Planes      289
Weintraub Symplectic Pairs/Hall Planes      635
Weyl group      760
Witt index      768
Witt’s Lemma      768
Witt’s Theorem      766
Y-Shears Group      326
‘All Except’ Replacement Theorem      128
‘Spreading’ Theorem      586
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