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

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Ќазвание: Handbook of Finite Translation Planes

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

јннотаци€:

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

–убрика: ћатематика/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 2007

 оличество страниц: 861

ƒобавлена в каталог: 08.05.2008

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
$G/H^2$-Nest      473
$G/H^2$-Nest of Reguli      473
$\lambda$-System      171
$\sigma$-Associated Spread Sets      265
$\sigma$-Regulus      259
(A,B)-Regular Spreads      555
(g, f)-Quasi-Spread-Set      264
(K, L)-Isomorphism      9
(k,t)-Nest      491
(k,t)-Nest Replaceable      491
(q + 1)-Arc      338
(q + 1)-Nest      474
(q - 1)-Nest      473
(T,BH)-Spreads      365
(T,EH)-Spreads      365
1/4-Fano Theorem of Fisher Ч Johnson      212
12-Nest Planes of Johnson Ч Prince      742
2/3-Transitive Axial Groups      531
3/2-Transitive group      517
3/8-Theorem for Andre Planes      214
5th Cousin of a Semifield Flock Spread      623
A(5)-Slices      246
Abatangelo and Larato Constructions      190
Adelaide Flocks      437
Adelaide Skeleton      439 798
Adelaide Super Skeleton      440 442 798
Affine Plane Generated by a Substructure      22
Albert Planes      74
Albert Product      74
Algebraic and Geometric Lifting      709
Algebraic Lifting Theorem      263
Algebraically Lifted Semifields      277 792
Algebraically Lifted Spread      709
Algebraically Lifted Spreads      263
Almost Linear Skeletons      441
Alternating Forms      764
Ambient Space      7
Andre Flat Flocks      566
Andre Method      26
Andre Planes      169 793
Andre Subgeometry Partitions      726
Andre Symplectically Paired Spreads      638
AndreТs Isomorphism Theorem      10
Anisotropic Orthogonal Space      774
Antipodal Covers and Twisted Fields      80
Automorphism Group of a Spread      10
Autotopism of a Pre-Quasifield      36
Autotopism of a Pre-Quasifield, Group      36
Axis of a Generalized Elation      323
Bader Ч Cossidente Ч Lunardon Theorem (A,B)-Regular      564
Bader Ч Lunardon Ч Pinneri Semifield Plane      277 792
Bader Ч Lunardon Ч Pinneri Spread      630
Bader Ч Lunardon Ч Thas BLT-Theorem      417
Bader Ч Marino Ч Polverino Ч Trombetti Theorem      387
Baer Axis      403
Baer Coaxis      403
Baer Group      398
Baer Subgeometry Partition      677
Baer-Elation Incompatibility      333
Baker Ч Ebert Double Nest Planes      479
Baker Ч Ebert Nest Planes      477
Baker Ч Ebert Ч Penttila Hyperbolic Fibration Theorem      418 449 570
Barriga/Cohen Ч Ganley/Kantor/Payne Skeleton      439 798
Bartolone Ч Ostrom Planes      115
BartoloneТs Theorem      351
Base Reguli for a Group G      473
BDDKLS-Theorem (Buekenhout et al.)      503 784 790
BEL-Flocks (Ball Ч Ebert Ч Luyckx)      456
Betten Skeleton      439 798
Bilinear forms      763
Biliotti Ч Jha Ч Johnson 2-Transitive Parabolic Ovals      536
Biliotti Ч Jha Ч Johnson 5th-Cousin Theorem      623
Biliotti Ч Jha Ч Johnson p-Primitive Parallelisms Theorem      237
Biliotti Ч Jha Ч Johnson PSL(2,q)-Theorem      346
Biliotti Ч Jha Ч Johnson Rank 3 Semifield Theorem      540
Biliotti Ч Jha Ч Johnson Theorem on Parabolic Ovals      535
Biliotti Ч Jha Ч Johnson Theorem on Quartic Groups      512
Biliotti Ч Jha Ч Johnson Theorem on Symplectic Flocks      622
Biliotti Ч Jha Ч Johnson Theorems Large Quartic Groups      510
Biliotti Ч Jha Ч Johnson Ч Menichetti $q^2$-$q^2$ Theorem      426
Biliotti Ч Jha Ч Johnson Ч Montinaro Theorem on Unitals      536 673 675
Biliotti Ч Johnson Non-Solvable Rank 3 Theorem      542
Biliotti Ч Korchmaros Slices      246
Biliotti Ч Menichetti Plane of Order 64      353
Biliotti Ч Menichetti/Jha Ч Johnson Ч Wilke $q^2$-Theorem      355
Biliotti, Jha, Johnson Theorems on Quadric Groups      510
Binary Knuth Semifields      72
Blocking set      378
Blocking Set of Redei Type      378
BLT-Set      417
Boerner Ч Lantz Semifields      274
Bol Plane      399 516
Bol Plane Classification Theorem      530
Bonisoli Planes      402
Bonisoli Resolutions Ч Minskowski Planes      402
Bonisoli Ч Korchmaros Ч Szonyi Planes      190
Brauer Ч Nesbitt Theorem on Irreducible GF(q)SL(2,q)-Modules      342
Brown Ч Ebert Ч Luyckx Flock Theorem      457
Bruck Cover      318
Bruck Triple Planes      187
Bruck Ч Bose is Andr?e at Infinity      27
Bruck Ч Bose Method      26
Bruen Chains      471 485
Buekenhout Hyperbolic Unital      659
Buekenhout Ч Delandtsheer Ч Doyen Ч Liebeck Ч Saxl      540
Buekenhout Ч Metz Unital      658
BuekenhoutТs Theorem Parabolic Unitals      651
ButtnerТs Planes of Order 64      737
C-systems      171
Cameron Ч Knarr Theorem on Tubes      400
Caps in PG(3,q)      504
Cardinali Ч Polverino Ч Trombetti Semifields, Even      277 792
Cardinali, Polverino, Trombetti Theorem      274
Center and Radius of Finite Circles      485
Center of a Generalized Elation      323
Center of a Semifield      75 556
Chain of Order 11 of Capursi      487 795
Chain of Order 11 of Raguso      487 795
Chain of Order 17 of Baker Ч Ebert Ч Weida      488 796
Chain of order 9 of V. Abatangelo      487 795
Chain of Reguli      471
Chain of Reguli in PG(3,K)      471
Chains of Lifts      269
Chains of Orders 13, 17, 19, 23, 31, 37 of Heden      487 795
Chains of Orders 5, 7 of Bruen      486 794
Chains of Orders 7, 11 of Korchmaros      487 795
Chains of Orders 9, 25, 27 of Heden Ч Saggese      487 795
Character of a Quadric      778
Characterization of Multiply Hyper-Regulus Replacement      309
Charnes Slice      246
Charnes Ч Dempwolff Planes      192 247
Chuvaeva Ч Pasechnik Theorem      87
Circle Geometry over a Full Field      474
Circular Spread      599
Classical Inversive Plane      395
Classical Laguerre Plane      395
Classical Minkowski Plane      396
Classification 2-Transitive Groups      781
Classification Affine 2-Transitive Groups      82
Classification Luneburg SL(2, 3)-Planes      67
Classification Luneburg SL(2, 5)-Planes      66
Classification of Rank 2 Affine Planes      539
Classification Theorem of Bol Planes      530
Classification Theorem of Desarguesian Scions      616
CofmanТs Theorem on Double Transitivity      515
Cohen Ч Ganley Semifield      277 792
Cohen Ч Ganley Skeleton      439 798
Collineation Group as a Semidirect Product      11
Companion Reguli      476
Completely Regular Line Oval      642
Components of a Group Partition      5
Components of a Partial Spread      14
Cone Representations      117 119
Cone, Vertex, Nucleus of a Quadric      778
Congruence partition      6
Congruence Spread      407
Conical Flock Plane      414
Conical Flock Spread      414
Conical Partial Flock      396
Conical Partial Spread      397
Conical Spread      410
Conway Ч Kleidman Ч Wilson, Moorhouse Ovoids      246
Conway, Kleidman, Wilson Ovoids      246
Cooperstein Ovoid      246
Coordinate-Function Pair      264
Cordero Ч Figueroa $3^6$-Semifield      277 792
Cordero Ч Figueroa Semifields of Odd Order      277 792
Cordero Ч Figueroa Theorem      78
Coulter Ч Matthews Commutative Semifields      277 792
Coulter Ч Matthews Planar Function Planes      753
Coulter Ч Matthews Symplectic Spreads      277 792
Coupled Planes      289
Coupled Translation Planes      289
Coxeter graph      760
Crystallographic group      760
Cubic Chain      549
Cubic Extension of an Affine Plane      544
Cubic Extensions of Flag-Transitive Planes      546
Cubic Hyper-Regulus Planes of Jha Ч Johnson      317
Cubic Planes of Culbert Ч Ebert      317
Cubical Array      619
Cyclic Homology Plane      456
Cyclic Ostrom Plane      517
Cyclic Ostrom Spreads      518
Cyclic Semifield Spread Set      109
Cyclic Semifields      109 113
Cylic Parallelism of Prince in PG(3, 5)      235
De Clerck Ч Herssens Sporadic Skeletons      446 799
Deficiency of a Partial Flock      396
Deficiency of a Partial Parallelism      230
Deficiency-One Partial Hyperbolic Flocks      400
Degenerate Quadratic Form      777
Degree of a Partial Spread      14
DembowskiТs Theorem Planar Functions      751
Dempwolff Plane of Order 16      337 340
Dempwolff SL(2, 5)-Planes      192 247
Dempwolff Theorem on Large Baer Groups      344
Dempwolff Ч Guthmann Slices      246
DempwolffТs Cyclic Theorem on Generalized Twist      78
Denniston Parallelisms in PG(3, 8)      235
Derivable Affine Plane      47
Derivable Partial Spread      54
Derivable Set of Skew Parallelisms      369
Derivation in PG(3,q)      53 411
Derivation of the Irregular Nearfield Planes      173
Derivation set      47
Derived Conical Flock Spread      424
Derived Foulser Ч Ostrom Planes      195
Derived Generalized Andre Planes Jha Ч Johnson      169 793
Derived Johnson Ч Prince Planes of Order 81      742
Derived plane      48
Derived Prohaska Plane of Order 81      739 740
Derived Spread      412 424
Derived Spreads in PG(3,q)      54 412
Desarguesian Orthogonal Spread      593
Desarguesian Parallelism      228
Desarguesian plane      5
Desarguesian Scions      615
Desarguesian Scions of Kantor Ч Williams      506
Desarguesian Symplectic Spreads      590
Desirable Plane      353
Dickson Nearfield Plane      62
Dickson Nearfield Planes      169 793
Dickson Pair      61
Dickson Planes      61
DicksonТs Commutative Semifields      75
Different/Same-Net      481
Dimension of a Translation Plane      8
Direct Product of Affine Planes      226
Direct sum of quadratic forms      767
Disjoint Set of Poles      191
Divisible Design      393
Divisible Designs of Spera Ч Schulz      394
Double H-Nests      479
Double Retraction      693
Double-Nest      492
Doubly Transitive Parabolic Oval      535
Draayer Ч Johnson Ч Pomareda Theorem Triangle Transitive      527
DraayerТs Theorem Index 3 Homology Groups      159
Dual of a Semifield      620
Dual Spread      357 361 407
Dual translation plane      367 745
Durga Prasad Flag-Transitive Plane 81      506
Dye Ovoid      245
E-Elation Nets      261
E-Nest      474
E-Parabolic Derivable Net      261
E-Parabolic Line Spread      261
E-Regulus Net      261
Ebert Quadruple Planes      187
Ebert Quintuple Planes      189
Effective Reflection Group      759
Elation Identification Theorem, Subregular, The      200
Elation Matrix      325
Elation of a Partial Spread      325
Elation Sliding      632
Elation-Baer Incompatibility      323
Elliptic Partial Flock      396
Elliptic Partial Spread      397
Elliptic quadric      224 777
Elliptic Spread-Spread      382
Elusive Plane      353
Elusive Plane of Luneburg Ч Tits      353
Enea Ч Korchmaros Theorem      80 87 535
Enea Ч Korchmaros Theorem 2-Transitive Ovals      535
Even and Odd Circles      485
Exceptional Luneburg Planes      63
Expanding a Quadratic Form      601
Extension of a Flag-Transitive Plane      543
Extensions of Derivable Nets      359
Exterior power      223
F-Dimension      8
F-Subspreads      20
Fano Configuration      211
Fano Configurations in Andre Planes      213
Fano Configurations in Johnson Generalized Andre Planes      217
Fans      18
Figueroa Planes      756
FigueroaТs One-Half j-Planes      581
FigueroaТs Theorem on p-Primitive Groups      88
Fingerprint of a Matrix Spread Set      501
Fisher Flocks      434
Fisher Skeleton      439 798
Fisher Ч Johnson 1/4-Subregular Theorem      211
Fisher Ч Johnson 3/8-Subregular Theorem      214
Fixed Plane of a Group      20
Flag-Transitive 27 Narayana Rao Ч Kuppuswamy Rao      506
Flag-Transitive 49 Narayana Rao Ч Kuppuswamy Rao      505
Flag-Transitive Affine Planes      503 790
Flag-Transitive Construction Ч Ebert, Baker, Narayana Rao      505
Flag-Transitive Planes and Subgeometry Partitions      508
Flag-Transitive Planes of Baker Ч Ebert      505
Flag-Transitive Planes of Foulser      505
Flag-Transitive Planes of Kantor      506
Flag-Transitive Planes of Kantor Ч Suetake      506
Flag-Transitive Planes of Narayana Rao      505
Flag-Transitive Planes of Suetake      506
Flag-Transitive Scions      614 616
Flat Flock      560
Flock Derivation      424
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