Combinatorics of spreads and parallelisms:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Boca Raton, Fla. [u.a.]
CRC Press
2010
|
| Schriftenreihe: | Pure and applied mathematics
295 |
| Schlagwörter: | |
| Links: | http://media.obvsg.at/AC08329192-1001 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025907804&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Beschreibung: | Literaturverz. S. 633 - 641 |
| Umfang: | XXI, 651 S. |
| ISBN: | 9781439819463 1439819467 |
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Datensatz im Suchindex
| _version_ | 1819358860389908480 |
|---|---|
| adam_text | Titel: Combinatorics of spreads and parallelisms
Autor: Johnson, Norman L.
Jahr: 2010
Contents
Preface
xv
Part 1. Partitions of Vector Spaces 1
Chapter 1. Quasi-subgeometry Partitions 3
1. Collineation Groups of Translation Geometries 10
Chapter 2. Finite Focal-Spreads 15
1. Towers of Focal-Spreads 16
2. Focal-Spreads and Coordinatization 18
3. k-Cuts and Inherited Groups 20
4. Spread-Theoretic Dual of a Semifield 26
5. The Dual Semifield Plane 26
6. The Six Associated Semifields 29
7. Symplectic Spreads 32
8. Additive Focal-Spreads 35
9. Designs, and Multiple-Spreads 38
10. Focal-Spreads from Designs 39
Chapter 3. Generalizing André Spreads 43
1. A Primer on André Planes 44
2. r-(sn, ç)-Spreads 45
3. Multiple Extended Replacements 55
4. Large Groups on i-Spreads 57
Chapter 4. The Going Up Construction for Focal-Spreads 61
1. The Going Up Construction 63
2. Generalization to Partitions with Many Spread Types 65
3. Going Up-Direct Sums 69
Part 2. Subgeometry Partitions 71
Chapter 5. Subgeometry and Quasi-subgeometry Partitions 73
Chapter 6. Subgeometries from Focal-Spreads 83
1. k-Cuts of Subgeometry Partitions 83
x CONTENTS
2. Additive k-Cuts 85
3. Right/Left Focal-Spreads 86
4. Hyperplane Constructions 88
Chapter 7. Extended André Subgeometries 91
Chapter 8. Kantor s Flag-Transitive Designs 97
1. Kantor s Class I 97
2. Kantor s Class II 99
3. mth-Root Subgeometry Partitions 101
4. Subgeometries from Kantor s Class I 101
5. Subgeometries from Kantor s Class II 104
Chapter 9. Maximal Additive Partial Spreads 111
1. Direct Sums of Semifields 114
2. Subfields of Order 4 in Knuth Semifields 117
3. The Commutative Kantor Semifields 120
Part 3. Subplane Covered Nets and Baer Groups 125
Chapter 10. Partial Desarguesian i-Parallelisms 127
1. A Primer on Subplane Covered Nets 127
2. Projective Spreads and Affine Nets 130
Chapter 11. Direct Products of Affine Planes 141
1. Desarguesian Products 144
2. Left Spreads and Left Partial Spreads 147
3. Desarguesian Left Parallelisms—Right Spreads 150
Chapter 12. Jha-Johnson SL(2, q) x C-Theorem 155
Chapter 13. Baer Groups of Nets 163
1. Left and Right in Direct Product Nets 165
2. Point-Baer Subplanes in Vector Space Nets 170
3. Translation Planes with Baer Groups 178
4. Spreads in PG(S, K) 187
Chapter 14. Ubiquity of Subgeometry Partitions 195
1. Jha-Johnson Lifting Theorem 196
2. Double-Baer Groups 201
3. Fusion of Baer Groups 203
4. Double-Homology Groups 206
5. Dempwolff s Double-Baer Groups 208
6. Subgeometry Partitions from Going Up 210
7. Algebraic Lifting of Focal-Spreads 211
CONTENTS xi
Part 4. Flocks and Related Geometries 215
Chapter 15. Spreads Covered by Pseudo-Reguli 217
1. Pseudo-Reguli 217
2. Conical and Ruled Spreads over Skewfields 223
Chapter 16. Flocks 231
1. Conical Flocks 231
2. Hyperbolic Flocks 235
3. Partial Flocks of Deficiency One 240
4. Point-Baer Groups and Partial Flocks 240
5. Deficiency One Partial Conical Flocks 242
6. Deficiency One Partial Hyperbolic Flocks 246
7. The Theorem of Johnson, Payne-Thas 250
Chapter 17. Regulus-Inducing Homology Groups 253
Chapter 18. Hyperbolic Fibrations and Partial Flocks 267
Chapter 19. j-Planes and Monomial Flocks 273
1. Hyperbolic Fibrations over the Reals 277
2. Classification of the Real j-Planes 281
Part 5. Derivable Geometries 285
Chapter 20. Flocks of a-Cones 287
1. Maximal Partial Flokki and a-Flocks 290
2. Deficiency One and Baer Groups 293
3. if-Flokki and Algebraic Lifting 294
4. Net Replacement in the Hughes-Kleinfeld Planes 295
Chapter 21. Parallelisms of Quadric Sets 301
1. The Thas, Bader-Lunardon Theorem 302
2. Parallelisms of Hyperbolic Quadrics 303
3. Bol Planes 305
4. Parallelisms of a-Cones 309
Chapter 22. Sharply ¿-Transitive Sets 313
1. Subsets of PTL(n, K) 314
2. Subsets in FTL(n, q) of Deficiency 1 317
3. The Parallelisms of Bonisoli 322
Chapter 23. Transversals to Derivable Nets 327
1. Algebraic Extensions of Derivable Nets 328
2. Geometric Extension of Derivable Nets 330
3. Planar Transversal Extensions 332
xii CONTENTS
4. Semifield Extension-Nets 337
Chapter 24. Partially Flag-Transitive Affine Planes 345
1. Derivable Affine Planes with Nice Groups 350
Chapter 25. Special Topics on Parallelisms 365
1. Transversal Spreads and Dualities of PG(3, K) 365
2. Skew Parallelisms 365
Part 6. Constructions of Parallelisms 369
Chapter 26. Regular Parallelisms 371
1. Infinite Regular Parallelisms 371
2. The Set of 2-Secants 374
3. Isomorphisms of Transitive Parallelisms 377
4. Finite Regular Parallelisms 379
5. The Penttila-WiUiams Construction 380
Chapter 27. Beutelspacher s Construction of Line Parallelisms 387
1. Extension of Beutelspacher s Theorem 388
2. Applications of Beutelspacher s Construction. 391
Chapter 28. Johnson Partial Parallelisms 395
1. Isomorphisms 399
2. The Derived Parallelisms 411
Part 7. Parallelism-Inducing Groups 415
Chapter 29. Parallelism-Inducing Groups for Pappian Spreads 419
Chapter 30. Linear and Nearfield Parallelism-Inducing Groups 427
1. Parallelism-Inducing Subgroups of GL(2, q2) 431
2. The General Nearfield Parallelism-Inducing Group 433
3. Isomorphisms of Group-Induced Parallelisms 434
4. Nearfield Parallelism-Inducing Groups 436
5. Finite Regular Nearfield Groups 439
6. m-Parallelisms 441
Chapter 31. General Parallelism-Inducing Groups 449
1. The Isomorphisms of Kantor-Knuth Type Parallelisms 454
2. Finite Regulus-Inducing Elation Groups 457
3. Finite General Parallelism-Inducing Groups 461
4. Minimal Linear Parallelism-Inducing Groups 464
5. Relative Linear Parallelism-Inducing Groups 465
6. Existence of Minimal Groups 472
CONTENTS xiü
7. Determination of the Minimal Groups 475
8. General Isomorphisms from Minimal Groups 478
9. Isomorphic Kantor-Knuth Parallelisms 481
10. Even Order 484
11. Derived Parallelisms 486
Part 8. Coset Switching 489
Chapter 32. Finite ^-Switching 491
1. ?-and Desarguesian Switches 491
2. The Switches of Desarguesian Spreads 493
3. Coset Switching again with Desarguesian Spreads 496
4. An Upper Bound 499
5. Upper Bound, Even Order 502
Chapter 33. Parallelisms over Ordered Fields 507
Chapter 34. General Elation Switching 515
1. Deficiency One Transitive Groups 520
2. Switching Theorem over Ordered Fields 524
Chapter 35. Dual Parallelisms 529
1. The Isomorphisms of the Dual Parallelisms 534
Part 9. Transitivity 543
Chapter 36. p-Primitive Parallelisms 545
1. Biliotti-Jha-Johnson p-Primitive Theorem 546
2. Transitive Parallelisms 552
3. Biliotti, Jha, Johnson—Transitive Classification 552
4. Johnson s Classification of 2-Transitive Parallelisms 552
Chapter 37. Transitive t-Parallelisms 555
1. Johnson-Montinaro t-Transitive Theorem 555
2. Transitive Parallelisms of PGL(2r - 1,2) 555
3. Isomorphisms of the Transitive Parallelisms 559
Chapter 38. Transitive Deficiency One 561
1. BJJDJM-Classification Theorem 561
2. Deficiency One—The Spreads Are Isomorphic 576
3. The Full Group 576
Chapter 39. Doubly Transitive Focal-Spreads 583
1. Johnson-Montinaro; Elementary Abelian Case 585
xiv CONTENTS
Part 10. Appendices 591
Chapter 40. Open Problems 593
1. Non-standard Groups and Non-standard Parallelisms 594
Chapter 41. Geometry Background 609
Chapter 42. The Klein Quadric 613
1. The Thas-Walker Construction 614
Chapter 43. Major Theorems of Finite Groups 617
1. Subgroups of PSL{2, q) 617
2. The Lists of Mitchell and Hartley 618
3. Finite Doubly Transitive Groups 620
4. Primitive Subgroups of FL(4, q) 620
5. Aschbacher s Theorem 621
6. Gurahiick-Penttila-Praeger-Saxl Theorem 623
7. O Nan-Scott Theorem 624
8. Dye s Theorem 625
9. Johnson-Montinaro i-Transitive Theorem 625
Chapter 44. The Diagram 631
Bibliography 633
Index 643
|
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.52 |
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| dewey-sort | 3512.52 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV040928816 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T16:27:24Z |
| institution | BVB |
| isbn | 9781439819463 1439819467 |
| language | English |
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| physical | XXI, 651 S. |
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| publisher | CRC Press |
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| series2 | Pure and applied mathematics |
| spellingShingle | Johnson, Norman L. 1939- Combinatorics of spreads and parallelisms Pure and applied mathematics Inzidenzgeometrie (DE-588)4162265-0 gnd Vektorraum (DE-588)4130622-3 gnd Projektive Geometrie (DE-588)4047436-7 gnd |
| subject_GND | (DE-588)4162265-0 (DE-588)4130622-3 (DE-588)4047436-7 |
| title | Combinatorics of spreads and parallelisms |
| title_auth | Combinatorics of spreads and parallelisms |
| title_exact_search | Combinatorics of spreads and parallelisms |
| title_full | Combinatorics of spreads and parallelisms Norman L. Johnson |
| title_fullStr | Combinatorics of spreads and parallelisms Norman L. Johnson |
| title_full_unstemmed | Combinatorics of spreads and parallelisms Norman L. Johnson |
| title_short | Combinatorics of spreads and parallelisms |
| title_sort | combinatorics of spreads and parallelisms |
| topic | Inzidenzgeometrie (DE-588)4162265-0 gnd Vektorraum (DE-588)4130622-3 gnd Projektive Geometrie (DE-588)4047436-7 gnd |
| topic_facet | Inzidenzgeometrie Vektorraum Projektive Geometrie |
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