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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
Linear Subset of Hyper-Reguli      317
Locally Hermitian Ovoid      380
Locally Hermitian Spread of an Elliptic Quadric      381
Locally Hermitian Translation Ovoid      380
Locally Hermitian Translation Spread      381
Lorimer — Rahilly Plane      233 757 801
Luneburg — Tits Planes      245 547 630 794
Luneburg’s Characterization Theorem for Generalized Andre Planes      532
Luneburg’s SL(2, n)-Theorem      532
Luneburg’s Theorem Generalized Andre Planes      532
m-Ovoids of Generalized Quadrangles      640
Maschietti’s Line Oval-Design Theorem      642
Maschietti’s Theorem on Line Ovals      642
Mason — Ostrom Planes      247
Mason — Shult Planes/Slices      247
Mathon Plane of Order 16      757 802
Matrix Spread Set      410
Maximal Kernel Subspread      21
Maximal Partial Spread      13 405
Menichetti’s Characterization Generalized Twisted      74
Middle nucleus      75
Middle Seminucleus      556
Middle-Nucleus Semifields (Distortion-Derivation)      278 792
Mixed Nest      482
Mixed Nests      480
Mondello Family      445 799
Mondello Sporadic Skeletons      446 799
Monomial Skeletons      441
Moorhouse Affine Planes of Order 25      758 802
Moorhouse Ovoids      246
Multiple Andre Replacement      179
Multiple Generalized Andre Planes of Ostrom      169 793
Multiple Hyper-Regulus Planes of Jha — Johnson      303
Multiple Nest      491
Multiple Retraction      693
Mutually Orthogonal Spaces      764
n-Dimensional Orthogonal Group      759
Nagagawa Slices      247
Narayana Rao — Rodabaugh — Wilke — Zemmer Planes      172
Narayana Rao — Satyanarayana Skeleton, Characteristic-5      439 798
Narayana Rao, Kuppuswamy Rao Order-125 Plane      506
Narayana Rao, Kuppuswamy Rao, Durga Prasad Order-81 Planes      506
Narayana Rao, Kuppuswamy Rao, Satyanarayana Order-27 Planes      506
Natural Basis for a Derivable Net      259
Near Nearfield Planes      526
Nearfield Plane      60
Nest Group      473
Non-Linear Set of Reguli      185
Non-Solvable Identification Theorem, Subregular      200
Non-solvable Rank k Affine Plane      539
Normal Line Spread      383
Normal Partition      5
Nuclei      44
Nuclei and Groups in Generalized Twisted Field Planes      82
Nucleus      75
Nucleus of a Line Oval      641
Nucleus of a Semifield      556
Omnibus Flock Theorem, The      627
Opposite regulus      48
Opposite Regulus in PG(3,q)      411
Orbit Lengths of the Dempwolff Plane      341
Origin of a Spread      7
Orr Spread      188
Orthogonal array      117
Orthogonal complement      764
Orthogonal group      759
Orthogonal Set of Skew Parallelisms      369
Orthogonal Space      766
Orthogonal Spread      584
Orthogonal Spreads of Desarguesian Spreads      617
Orthogonal subspace      759
Orthogonal sum      767
Osculating plane      339
Ostrom Dimension      782
Ostrom Phantom      782
Ostrom Semi-Translation Planes of Type 1      748 801
Ostrom — Foulser Planes      187
Ostrom — Rosati Planes      755
Ostrom — Wagner theorem      749 750
Ostrom-Derivates      421
Ostrom/Johnson — Seydel Spread      186
Ostrom’s 1st and 2nd Generalized Andre Constructions      169 793
Ostrom’s 1st Replacement Theorem      127
Ostrom’s 2nd Replacement Theorem      128
Ostrom’s Baer Trick      782
Ostrom’s Critical Degree Theorem      784
Ostrom’s Elation Theorem      329
Ostrom’s p-Prime Theorem      782
Ostrom’s Phantom Theorem      55 782
Ott — Schaeffer Planes      338
Oval Cone      118 338
Oval in a Projective Plane      641
Oval Laguerre Plane      395
Oval Tube in PG(3,q)      400
Ovoid      241
Ovoid in PG(3,q)      395
Ovoid of Klein Quadric      223
Ovoidal Inversive Plane      395
Oyama Method      283
P-Regular Line Oval      642
Pabst — Sherk Planes      388
Parabolic Elation Group      261
Parabolic Oval      535
Parabolic point      535
Parabolic Quadric      777
Parabolic Unital      650
Parallel Class for a Translation Net      16
Parallelism      225
Parallelisms in PG(3, 2), The      232
Partial Flag-Transitive Plane      367
Partial Flock of Elliptic Quadric      396
Partial Flock of Hyperbolic Quadric      396
Partial Flock of Minkowski Plane      396
Partial Flock of Oval Laguerre Plane      395
Partial Flock of Ovoidal Inversive Plane      395
Partial Flock of Quadratic Cone      396
Partial Flock of Quadric Set      396
Partial Parallelism      229
Partial spread      13 14
Partial Spread Net      16
Partial Spread of Quadratic Type      397
Partial Tube in PG(3,q)      400
Partially Flag-Transitive Affine Planes      370
Payne — Rogers Recoordinatization Theorem      424
Payne — Thas Symplectic Spread      277 630 792 794
Penttila Flocks      433
Penttila Skeleton      439 798
Penttila — De Clerck Sporadic Skeletons      446 800
Penttila — Royle Sporadic Skeletons      446 799
Penttila — Williams 5th Cousin      626
Penttila — Williams Desarguesian Parallelisms      235
Penttila — Williams Symplectic Spread      277 626 630 792 794
Penttila, Storme / Johnson j-Theorem      574
Planar Function      751
Planar Group      20
Planar Set of Skew Parallelisms      369
Planar Transversal Spread      358
Planes Coupled with Semifield Planes      293
Planes with Many Elation Axes      219
Polarizing Bilinear Form      766
Pre-Quasifield      30 36
Pre-Semifield      42
Primitive Groups of $\Gamma L(4,q)$, The      781
Primitive Plane      518
Prince Parallelisms in PG(3, 3)      232
Prohaska Plane of order 81      739
Prohaska Planes      189
Prohaska SL(2,5)-Planes      190
Projective Index of a Quadric      778
Projective unitary group      379
q-Clan      417
q-Fan      178
q-Nest      474
Quadratic Cone      395
Quadratic Extension of an Affine Plane      544
Quadric      766
Quadric Set      396
Quartic Axis      509
Quartic Extension of an Affine Plane      544
Quartic Extensions of Flag-Transitive Planes      550
Quartic Group      509
Quartic Groups with Index      509
Quasi-Subgeometry      716
Quasi-Subgeometry Partition      717
Quasi-Subgeometry Partitions from Fans      728
Quasifield      29 36
Radical      768
Rank and Index of a Cone Representation      119
Rank k + 1 Groups      517
Rank k Affine Plane      539
Rational Desarguesian Net      556
Rational Desarguesian Partial Spread      23 250
Rational Partial Spread      23
Rational Partial Spread across W      23
Rational Partial Spread Determined by W      23
Ree — Tits Ovoids and Slices      243
Reflection      759
Reflection along r      759
Reflection through P      759
Reflexive Bilinear Form      764
Regular Hyperbolic Fibration      418
Regular Hyperbolic Fibration with Constant Back Half      418
Regular Nearfield Plane      60
Regular Oval Tube      400
Regular Parallelism      228
Regular tube      400
Regulus      48
Regulus Hyperbolic Cover      577
Regulus in PG(3,q)      411
Regulus Partial Spread, The      411
Regulus Question      49
Regulus-Inducing Elation Group      415 569
Residue of a Point of an Inversive Plane      395
Retraction Spread Set      267
Retractions      265
Right nucleus      75
Right Seminucleus      556
Rigid Skeletons      443
Rigid Translation Plane      747
Roman Son, The (Payne — Thas)      625
Root system      759
Rotation group      597
Royle Subregular Plane      201
Ruling Class of a Hyperbolic Quadric      779
s-Inversion      424
s-Inversion of a Conical Spread      412 425
s-Square of a Conical Spread      413 425
Same/Different-Nets      481
Sandler Semifields      277 792
Schaeffer — Walker SL(2,q)-Theorem      341
Segre variety      563
Self-Transposed Spreads      634
Semi-Translation Plane      334 745
Semi-Translation Planes of Type i      747
Semi-Translation Planes of Types q + 1 and 2      747
Semifield      42 556
Semifield Center Is a Geometric Invariant      98
Semifield Flat Flocks      565
Semifield Skeletons      440
Semilinear Group as the Stabilizer of 0      11
Seminuclear Homology Group      94
Seminuclei      75 556
Seminuclei of a Semifield      91
Set-Transpose Spreads      634
Sharply Transitive Set      401
Sharply Transitive Sets and Translation Planes      59
Shear      46
Shears Spread      46
Sherk Plane of Order 27      737
Sherk Surfaces      318
Sherk’s Indicator Theorem      390
Short Hermitian Sequence      382
Shult Ovoid      246
Shult Set      380
Shult — Lunardon Theorem Locally Hermitian Ovoids      381
Similarity      767
Simple Full Non-Square Andre Plane      293
Singer cycle      504
Singular hyperplane      586
Singular Orthogonal Space      777
Singular Part of a Totally Isotropic Space      584
Skeleton of a Flock      421
Skew Parallelism      369
Skew Quartic Groups      514
Skew symmetric matrix      584
SL(2, 3)-Luneburg Planes      66 464
SL(2, 5)-Hiramine Planes      67
SL(2, 5)-Luneburg Planes      64 464
Slices of Conway — Kleidman — Wilson Ovoids      248
Slices of the Unitary Ovoids, The      241
Slicing an Orthogonal Spread      585
Small-Deficiency Maximal Partial Spread      405
Solvable Extension      544
Solvable Extensions of Flag-Transitive Planes      551
Solvable Rank k Affine Plane      539
Sperner Space      7 407
Splitting Normal Partition      6
SPREAD      5 7
Spread Components      7
Spread from Quasifield, Spread Associated to Q      37
Spread Isomorphism      9
Spread of an Elliptic Quadric      381
Spreading a Spread      585
Spreads in PG(3,q)      409
Square and Non-Square Andre Nets      474
Stability Group of a Ryper-Regulus      317
Stable Group      517
Standard Circle      476
Standard Form of a Regulus      411
Standard Regulus      414
Standard Regulus Net      476
Standard Representations of GL(2, K) and SL(2,K)      327 328
Strongly Orthogonal KW-System      601
Strongly Orthogonal Spread      607
Strongly regular graph      640
Sub(Partial) Spread      19
Subgeometry      716
Subgeometry Partition      677 717
Subiaco Skeleton      440 798
Subnets of Translation Nets      16
Subpartial Spread      15
Subpartial Spreads across Subspaces      19
Subregular Lifting      180
Subregular Lifting and Fano Configurations      213
Subregular Translation Plane      398
Suetake Planes      287
Suetake Symplectic Spreads      630 794
Symmetric Homology Groups      159
Symmetric Spread Representation      631
Symplectic Bilinear Forms      763
Symplectic Extension Theorem      585
Symplectic Flocks      621
Symplectic Generalized Twisted Field Planes      630 794
Symplectic group      589
Symplectic Pairs      636
Symplectic Polarity      589
Symplectic Slice of Ree — Tits Ovoids      630 794
Symplectic Spreads      585
Symplectic Translation Ovoid      644
Symplectically Paired Spreads      636
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