Johnson M., Jha W., Biliotti M. — Handbook of Finite Translation Planes :: Электронная библиотека попечительского совета мехмата МГУ

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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

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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

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Предметный указатель

Flock Generalized Quadrangle      417
Flock of a Minkowski Plane      396
Flock of an Oval Laguerre Plane      395
Flock of an Ovoidal Inversive Plane      395
Flocks of the Minkowski Planes M(a,b)      402
Foulser — Johnson Theorem      193 341 519 783
Foulser — Johnson — Ostrom Theorem      342
Foulser — Ostrom Planes      195
Foulser-Cover      24
Foulser’s Baer Group Theorem      422
Foulser’s Baer-Elation Incompability Theorem      236 333
Foulser’s Planes of Order 81      744
Foulser’s Solvable Flag-Transitive Theorem      785
Foulser’s Theorems on Baer Groups      784
Full Field      472
Fundamental Hyper-Reguli of Jha — Johnson      297 300
Fundamental Identification Theorem-Subregular      199
Fundamental Reflections      760
Fundamental Roots      760
Fundamental Theorem on Generalized Elations      324
Fundamental Theorem on Generalized Twisted Fields      77
Fundamental Theorem on Symplectic Spreads      589
Fundamental Theorem on Translation Planes      11
Fusion of Nuclei in a Semifield      558
Ganley Commutative Semifields      277 792
Ganley Symplectic Spreads      277 792
Ganley — Jha Theorem      78 87
Ganley — Jha — Johnson Theorem      520 784
Ganley — Jha — Johnson Theorem on 2-Transitive Groups      515 541
Gardiner’s Theorem, Distance-Transitive Graphs      87
General Indicator Sets      390
General Semifield 5th Cousins      627
General Spread      407
Generalized Andre Flat Flocks      568
Generalized Andre Planes of Draayer      169 793
Generalized Andre Planes of Draayer — Johnson — Pomareda      169 793
Generalized Andre Planes of Foulser      169 793
Generalized Andre Planes of Hiramine — Johnson      169 793
Generalized Andre Planes of Johnson      169 793
Generalized Andre Planes of Narayana Rao — Zemmer      169 793
Generalized Andre Planes of Ostrom      125
Generalized Andre Planes of Wilke      125 126 169 793
Generalized Andre Planes of Wilke — Zemmer      169 793
Generalized Andre Replacements of Johnson      154
Generalized Dickson Semifields      277 792
Generalized Elation      323
Generalized Knuth Spreads      364
Generalized Partial Spread      18
Generalized Quadrangle of Order (s, t)      415
Generalized Spread      407
Generalized Twisted Field Flat Flocks      565
Generalized Twisted Field Isomorphism Theorem      84
Generalized Twisted Fields      73 277 792
Geometric Extension      360 361
Gevaert — Johnson “Regulus-Inducing” Flock Theorem      423
Gevaert — Johnson — Thas Theorem on Conical Flocks      415 417
GF(q)-Linear Set      644
GJDLCF-Theorem      88 533
GL(2, 3)-Spread Order 25      186
Glynn’s Theorem on Cone Representations      119
Glynn’s Theorem on Cone Representations of Affine Planes      120
Group Partition      5
Group Replaceable Translation Plane      473
Group-Regulus Net      482
Hall plane      48 338 469
Hall Planes of Order 9      61
Heden’s Theorem on Replaceable Bruen Chains      471
Heimbeck Planes      469
Hemisystem      640
Herd of Hyperovals      418
Hering Plane of Order 27      504
Hering Planes      338
Hering Symplectic Spread      630 794
Hering — Ostrom Theorem      330 783
Hering — Schaeffer/Grundhofer — Figueroa Planes      756
Hering’s Flag-Transitive Theorem      785
Hering’s Plane of Order 27      390
Hering’s Theorem on 2-Transitive Groups      516 787
Hermitian form      379
Hermitian polarity      379
Hermitian Sequence of Elliptic Type      382
Hermitian Sequence of Hyperbolic Type      383
Hermitian Surface      379
Hiramine Cubic Planes      287
Hiramine — Jha — Johnson Theorem on Flag-Transitive Extensions      545
Hiramine — Johnson Theorem Index 2 Homology Groups      159
Hiramine — Johnson Theorem on Index 2 Homology      403
Hiramine — Johnson/Draayer — Index 2-Generalized Andr?e      160
Hiramine, Jha, Johnson Classification of Quadratic Extensions of Flag-Transitive Planes      545
Hiramine, Jha, Johnson Theorems on Cubic Extensions      546
Hiramine, Johnson / Draayer — Two Homology      525
Hiramine/Keiser Theorem on Primitive Planes      518
Hiramine’s Theorem $SL(2,5)\times SL(2, 5)$ -Planes      68
Hiramine’s Theorem on 2-Transitive Groups      519
Hits and Misses of Reguli      476
Hofer’s Theorem      671
Homology Group-Flock Theorem of Johnson      569
Hughes Planes      755
Hughes — Kleinfeld Semifields      75 277 699 792
Hyper-Oval      641
Hyper-Regulus      153
Hyper-Regulus Planes of Dover      320
Hyper-Regulus Planes of Jha — Johnson      301
Hyperbolic Cover      93 95 556
Hyperbolic Fibration      418 570
Hyperbolic Fibration of Dimension n      576
Hyperbolic line      770
Hyperbolic Partial Spread      397
Hyperbolic plane      770
Hyperbolic quadric      223 777
Hyperbolic Unital      650
Hyperplane Spread      407
i/3-Triangle Transitive Plane      531
Indicator Set      374
Indicator Set of       390
Indicator Sets = Transversals to Derivable Nets      375
Indicator Space      373
Indicator Spread      376
Induced Partial Spread      19
Induced Quasi-Subgeometry      716
Induced Subgeometry      716
Intersection Subspread      22
Inversing Replacements      294
Inversive plane      393
Irreducible Coxeter Group      760
Irreducible GF(p)SL(2,q)-Modules      343
Irregular Hughes Planes      756
Irregular Nearfield Planes      60 246 480
Irregular Nearfield planes with Non-Solvable Group      60
Irregular Nearfield planes with Solvable Groups      60
Irregular Nearfields      60
Isometry      767
Isotopism      36
Isotopism of Pre-Quasifields      36
j, k-Planes      576
j-Plane      560 573
j. ..j-Plane      560 569 576
Jha — Johnson ( - ) Plane of Order 64      354
Jha — Johnson 2-Transitive Skeleton Theorem      422
Jha — Johnson Algebraic & Geometric Lifting Theorem      711
Jha — Johnson Baer-Elation Incompatibility Theorems      236 334 345
Jha — Johnson Canonical Action GL(2,q)-Theorem      193
Jha — Johnson Coupling Theorem      293 639
Jha — Johnson Cyclic Parallelism Theorem      236
Jha — Johnson Cyclic Semifields      277 792
Jha — Johnson Cyclic Semifields Type S(w,m,n)      110
Jha — Johnson Cyclic Semifields — p-Primitive Type 1      110
Jha — Johnson Cyclic Semifields — q-Primitive Type 2      110
Jha — Johnson Derived Generalized Andre Planes      165
Jha — Johnson GL(2,q)-Planes      113 115

Jha — Johnson Hyper-Regulus Construction Theorem      305
Jha — Johnson Large Double Baer Group Theorem      345
Jha — Johnson Overlap Theorem      744
Jha — Johnson q(q+1)-Theorem      468 493 496
Jha — Johnson q/2-Elation Spread Order 64      188
Jha — Johnson Theorem on Baer Group Pairs      422
Jha — Johnson Theorem on Cyclic Desarguesian Parallelisms      194
Jha — Johnson Theorem on Cyclic Ostrom Spreads      518
Jha — Johnson Theorem on Foulser — Ostrom Planes      194
Jha — Johnson Theorem on Generalized Desarguesian Planes      113
Jha — Johnson Theorem on Hyperbolic Covers      557
Jha — Johnson Theorem on Large Baer Groups      345
Jha — Johnson Theorem on Nuclear Fusion      92 100 107
Jha — Johnson Theorem on Parabolic Unitals      672
Jha — Johnson Theorem on SL(2,5) order 81      743
Jha — Johnson Theorem on Transitive Semi-field Flat Flocks      561 565
Jha — Johnson Theorem on Ubiquity of Maximal Partial Spreads      406
Jha — Johnson “Moved” Spreads      189
Jha — Johnson — Wilke Extension of Bartolone      355
Jha’s Tangentially Transitive Theorem      786
Johnson 2-Transitive Parallelism Theorem      537
Johnson Generalized Andre Planes      153
Johnson Hyper-Regulus Quasi-Subgeometry Partitions      731
Johnson Plane of Order 16, The      757 802
Johnson Quasi-Subgeometry Partitions      733
Johnson Semi-Translation Planes of Type 1      748 801
Johnson — Huang Semifields Order 64      277 792
Johnson — Kallaher/Luneburg Rank (k,k)-Theorem      539
Johnson — Marino — Polverino — Trombetti Non-Cyclic Semifield of Order       277 282 792
Johnson — Marino — Polverino — Trombetti Semi-fields      277 792
Johnson — Payne — Thas Baer-Flock Theorem      495
Johnson — Pomareda Many Homology Theorem      461
Johnson — Pomareda Mixed Nest Planes      480
Johnson — Pomareda Theorem on Buekenhout — Metz      657
Johnson — Pomareda Theorem on Large Unital Groups      657
Johnson — Pomareda Theorem on Unitals      664
Johnson — Pomareda Theorem on Unitals with Large Groups      657
Johnson — Pomareda Two Cyclic Homology Theorem      461
Johnson — Prince Planes of Order 81      739 741 742
Johnson — Vega Homology Groups Symplectic Flock Theorem      634
Johnson — Vega — Wilke j,k-Planes      577
Johnson — Walker Plane      233 757 801
Johnson — Wilke - Theorem      427
Johnson — Wilke — Lunardon Theorem-Skeletons      537
Johnson, Marino, Polverino, Trombetti Theorem      275
Johnson/Payne — Thas Baer-Elation Flock Theorem      415
Johnson’s 1/4-Theorem for Generalized Andre      217
Johnson’s 2-Transitive Parallelism Theorem      236
Johnson’s Classification 2-transitive Parallelisms      236
Johnson’s Classification Derivable Subregular      208
Johnson’s Classification Theorems for t-Nests      483
Johnson’s Cyclic Homology-Conical Flock Theorem      419
Johnson’s Homology Theorem for Hyperbolic Fibrations      452
Johnson’s Non-Solvable Triangular Transitive Theorem      528
Johnson’s Ostrom Phantom Theorem      784
Johnson’s Reconstruction Theorem      369
Johnson’s Structure Theorem, Derivable Nets      53
Johnson’s Theorem on Bol Planes      530
Johnson’s Theorem on Cyclic Homology-Flocks      569
Johnson’s Theorem on Derivation of Dual Translation Planes      746
Johnson’s Theorem on Even-Order Semifield Flocks      426
Johnson’s Theorem on Fans and Quasi-Sub-geometries      718
Johnson’s Theorem on Group Replaceable Nests      473
Johnson’s Theorem on Partial Flag-Transitive Planes      370
Johnson’s Theorem on Partial Sharp and Double Baer      403
Johnson’s Theorem on Transitive Parabolic Unitals      650 653
Johnson’s Theorems on Deficiency-One Flocks      399
Johnson’s Theorems on Hyper-Regulus Constructions      731
Johnson’s Two Large Homology Theorem      462
Johnson—Pomareda Theorem on Transitive Buekenhout — Metz Unitals      658
K-Dimension of a Partial Spread      14
K-Linear Isomorphism of Partial Spread      15
K-Partial Spread      14
Kallaher — Hanson Theorem Bol Planes      529
Kallaher — Liebler Rank 3 Theorem      539
Kallaher — Ostrom Theorems Bol Planes      529
Kallaher — Ostrom — Hanson — Johnson Theorem Bol      530
Kallaher, Czerwinski — Schulz Theorem      32
Kallaher’s Theorem Bol Planes      529
Kantor -Planes      115
Kantor Likeable Skeleton      439 798
Kantor Symplectic Semifield Spreads      630 794
Kantor — Knuth Conical Spread      411
Kantor — Knuth Semifield      277 792
Kantor — Knuth Skeleton      439 798
Kantor — Knuth Symplectic Spread      630 794
Kantor — Williams Commutative Semifields      277 792
Kantor — Williams Desarguesian Scions      277 792
Kantor — Williams Spreads      599
Kantor — Williams Symplectic Semifield Spreads      630 794
Kantor — Williams Triple      599
Kantor’s 3rd Cousin      594
Kantor’s Theorem 2-Transitive Designs      515
KCLLS-Theorem on 2-Transitive Groups      533
Keiser’s Theorem on Primitive Groups      518
Kennzahl of a Matrix Spread Set      502
Kerdoc Sets      584
Kernel      6
Kernel Endomorphisms      6
Kernel Invariant Subspread      21
Kernel Subplane      20
Kernel Subspread      20
Klein Map      223
Klein quadric      223
Knarr/Johnson Geometric Extension Theorem      360
Knarr’s Theorem on Sharply Transitive Sets      402
Known Affine Planes of Order 25, The      758 802
Known Classes of Generalized Andre Planes      169
Known Classes of Semifields      277 792
Known Planes Not Translation Planes      758 802
Known Projective Planes of Order 16, The      757 801
Known Triangle Transitive Translation Planes, The      521
Knuth Binary Semifields      72 277 792
Knuth Semifields      277 792
Knuth Type j Semifields      102
KW-Triple      599
Laguerre plane      394
Large Quartic Groups      510
Latin square      117
Lattice      760
Lattice with Respect to a Basis      760
Lavrauw — Law BLT-set q = 167      447 801
Law BLT-sets q = 83      89 447 800
Law — Penttila Flocks      437
Law — Penttila Skeleton      439 798
Law — Penttila Sporadic BLT sets q < 130      446 800
Left nucleus      75
Left Seminucleus      556
Leitzahl of a Matrix Spread Set      502
Liebeck’s Theorem on Primitive Rank 3 Groups      786
Liebler SL(2, q)-Planes      115
Liebler’s Theorem on Sz(q)      532
Liebler’s Theorem, Distance-Transitive Graphs      87
Lift-Equivalent Quasifibrations      269
Lifted Desarguesian Spreads      268
Lifted Ganley Spreads      264
Lifted Generalized Knuth Semifield Spreads      264
Lifted Quasifibration      265
Lifted Spreads      261
Likeable Betten Plane      353
Likeable Plane      353
Likeable Plane of Kantor      353
Likeable Plane of Walker      353
Likeable Skeletons      441
Line Spread      383
Linear Collineations of Type t      323
Linear Hyper-Regulus Set      315
Linear Indicator Set      379
Linear Representation of       644
Linear Set of Reguli      185

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