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Biliotti M., Jha V., Johnson N. — Foundations of translation planes
Biliotti M., Jha V., Johnson N. — Foundations of translation planes

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Название: Foundations of translation planes

Авторы: Biliotti M., Jha V., Johnson N.

Аннотация:

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 coordinate 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.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2001

Количество страниц: 567

Добавлена в каталог: 01.12.2013

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
(g,f)-Quasi-spreadset      440
(K,L)-isomorphism      18
(q+l)-Arc      490
Affine contraction      510
Affine Elation      522
Affine elements      509
Affine Homology      522
Affine Linear Group      504
Affine Pappian Plane      505
Affine part      512
Affine plane      514
Affine Plane Generated by a Substructure      50
Affine Points      513
Affine Slices      512
Affine space      503
Affine Version      517
Affine-dimension      504
Affine-semilinear collineations      504
Albert Multiplier      164
Albert Multipliers      166
Albert Planes      396
Albert Product      395
Ambient Space      15
Andre plane      327
Andre System      326 327
Andre-kernel      215
Andre’s Homology Theorem      253
Automorphism Group of a Spread      19
Autotopism      150 188
Autotopism group      150 165
Autotopism Group of a Pseudoquasifield      188
Autotopism of a Binary System      164
Autotopism of a Pseudoquasifield      187
Axes of Coordinatization      97
Axis Identifier      103
Axis of a Central Collineation      521
Axis of a Generalized Elation      340
Baer chain of quasifields      309
Baer Condition for Quasifields      133
Baer Condition for Subplanes      132
Baer involution      522
Baer p-Group      287
Baer subplane      522
Base Skewfield      218
Base Subplane      279
Basis-Labeling      100
Bimodule      62
Binary Knuth Semifields      386
Binary Knuth Systems      384
Block-Parallel class      509
Block-Parallelism      509
Bruck-Bose      254
Center of a central collineation      521
Center of a Generalized Elation      340
Center of a Loop      169
Center of a Semifield      172
Central collineation      521
Central kernel      215 231
Centralizing Kernel      62
Chains of Lifts      464
Closed configuration      519
Coaxis of a Homology      111
Cocenter of a Homology      111
Collineation group      244 511
Collineation Group as a Semidirect Product      22
Complement of a Module      502
Component      71
Component Set      71
Components of a Group Partition      11
Components of a Partial Spread      41
Components of a Pseudospread      179
Composition of Isotopisms      165
Congruence partition      11
Conical Spread      28
Coordinate Labeling      97
Coordinate-Function Pair      440
Coordinatization by a (Partial) Quasifield      142
Coordinatization by Axes Identification      105
Coordinatization by Identification      96
Coordinatization by Labelling      96
Coordinatization Frame      142
Coordinatization Labeling      142
Coordinatization of a Partial Spreadset      97
Coordinatization of a Spreadset at e      186
Coordinatization Relative to a Basis      104
Coordinatization Relative to an Axes Identifier      103
Coordinatization Scheme      105
Coordinatizing (Partial) Spreadsets      136
Critical      483
Cyclic Maschke Split      256
Cyclic semifield spreadset      416
Cyclic Semifields      416
Degenerate Partial Plane      520
Degree of a Partial Spread      41
Dempwolff Plane      494
Derivable Affine Plane      265
Derivable Net      92
Derivable Partial Spread      267
Derivable Subnet      263
Derivation of a Regulus      270
Derivation set      265
Derived Affine Plane      263
Derived group      265
Derived Linespread      261
Derived Partial Spread      267
Derived plane      92 265
Derived Spread      32 267
Derived Spreads in PG(3,q)      30
Deriving a Regulus      270
Desarguesian Affine Plane      505
Desarguesian Projective Plane      507
Desarguesian projective space      507
Desarguesian Spread      65
Desarguesian Spreadsets      74
Dickson Nearfield      334 337
Dickson Pair      337
Dickson’s Commutative Semifields      398
Dilation      510
Dilation group      504
Dilation of an Affine Plane      522
Dimension of a Translation Plane      17
Distributive Pseudoquasifield      178
Dual incidence structure      508
E-Elation Nets      429
E-Parabolic Derivable Net      429
E-Parabolic Linespread      429
E-Regulus Net      429
Elation      521
Elation Matrix      345
Elation of a Partial Spread      345
Extensions of Modules      502
External Kernel      215 224
F-Dimension      17
F-Subspreads      48
Fixed Plane of a Group      47
Fixed-point-free group      298
Foulser-Cover      245 259 260
Frame      142
Free Planes      516
Frobenius complement      297 525
Frobenius group      297 525
Frobenius kernel      297 525
Fundamental Lamda-Law      320
G(set)-Orbit at x      60
Generalized Andre Plane      318
Generalized Andre System      318
Generalized Elation      340
Generalized Hall Plane      292
Generalized Twisted Field Planes      396
GL(2,q)-Spreads      417
GL(V,+)      501
GL(V,K)      499
Global Stabilizer of an Additive Subspace of a Partial Spreadset      81
Gradient      513
Gradient Geometry      70
Group Partition      10
Hall planes      490
Hall p’-subgroup      293
Hall quasifield      237
Hall Quasifields      233
Hall Spread      92
Hering Plane      490
Homology      521
Hughes Planes      315
Hughes — Kleinfeld Semifields      398
Incidence structure      508
Induced Binary System      165
Induced Partial Spread      45
Induced Partial Spreadset      82
Induced Structure related to a Pseudoquasifield      190
Inherited Group      265 267
Internal Kernel      215 220
Intersection Subspread      51
Intertwining map      219
Irreducible group      501
Irreducible KG-module      501
Isomorphic of Incidence Structures      508
Isomorphism of Partial Quasifields      129
Isotopic Binary Systems      164
Isotopism      164 187
Isotopism of Pseudoquasifields      187
K-Dimension of a Partial Spread      41
K-Linear Isomorphism of Partial Spreads      42
K-Partial Spread      41
K-Spreadset      61
Kernel      13
Kernel Endomorphisms      13
Kernel Homologies      522
Kernel Invariant Subspread      49
Kernel Planes on Desarguesian Nets      256
Kernel Subplane      48
Kernel Subspread      48
KG-module      501
KG-representation      501
Knuth conical-spread      29
Labeled Spreadset      183
Labeled System      183
Labelling Coordinatization Scheme      105
Lamda-Structure      318
Lamda-System      318
Left multiplier      164
Left nucleus      168
Left-Projective Space      506
Lift-Equivalent Quasifibrations      465
Lifted Ganley Spreads      444
Lifted Generalized Knuth Semifield Spreads      441
Lifted Pappian Spreads      459
Lifted Quasifibration      450
Lifted Spreads      430
Line-Baer Subplane      522
Linear Collineations of Type t      340
Linear group      499
Local Stabilizer of a Subspace of a Partial Spreadset      82
Locus      71
Long-loop Property      177
Loop      164
Lorimer-Rahilly Plane      314 480
Maschke-Complement      502
Matrix Spreadset      27 61
Maximal Kernel Subspread      49
Maximal Partial Spread      39
Maximal Tangentially Transitive Plane      468
Maximally Intersecting Baer p-Elements      365
Middle nucleus      168
Middle Nucleus Slopeset      200
Minimal Tangentially Transitive Plane      468
Mixed Tangentially Transitive Plane      468
Natural Basis for a Derivable Net      426
Nearfield      207
Normal Partition      11
Nucleus      168
Opposite Regulus in PG(3,q)      29
Opposite Skewfield      500
Order of a projective plane      523
Order of an affine plane      523
Origin of a Spread      15
Osculating plane      491
Ostrom — Rosati Planes      315
Ostrom’s Baer-Trick      301
Ott — Schaeffer Plane      490
Oval Cone      491
p-Planar Bound      310
p-Primitive collineation      299
p-primitive divisor      502
p-Primitive linear mapping      502
p-Primitive Theorem      502
Pappian Projective Plane      507
Parabolic Elation Group      429
Parallel affine subspaces      504
Parallel Class for a Translation Net      44
Parallel Classes of Affine Space      504
Parallel Lines in a Pseudoplane      179
Parallelism in Affine Planes      515
Partial K-Spreadset      67
Partial Plane      511
Partial Quasifield      120 122
Partial spread      39 41 243
Partial Spread Nets      44
Partial Spreads      39
Partial Spreadset      67
Period of a Lamda-System      325
Periodic Subgroup of a Generalized Andre System      326
Pi-Subgroup      293
Planar collineation      521
Planar Group      47
plane affine      514
Plane projective      515
Point-Baer Subplane      522
Point-Hyperplane Incidence Structure      508
Point-Line Incidence Structure      508
Prequasifield      176
Presemifield      178 384
Prime Subplane      153
Prime Subquasifield      153
Product of Isotopisms      165
Projection      102
Projective Automorphism Group      244
Projective closure      509
Projective closure of a group element      510
Projective dimension      506
Projective extension      514
Projective isomorphism      244
Projective plane      515
Projective space      506
Projective Spread      243
Pseudo quasifield      176
Pseudo-Regulus      245
Pseudoplane      179
Pseudoring      171
Pseudospread      179
p’-Subgroup      293
Quadrangle      511
Quadrangle Transitivity      518
Quadrilateral      511
Quasi-quasifield      442
Quasi-spreadset      439
Quasifibration      438 442
Quasifield      120 177
Quasigroup      164
Rational Desarguesian Partial Spread      53 404
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