Affine planes with transitive collineation groups:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York u.a.
North Holland
1982
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 155 S. graph. Darst. |
| ISBN: | 0444006206 |
Staff View
MARC
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| 245 | 1 | 0 | |a Affine planes with transitive collineation groups |
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Record in the Search Index
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|---|---|
| adam_text | CONTENTS
Preface xi
Standard Symbols xiii
chapter 1. PROJECTIVE PLANES AND AFFINE PLANES 1
Projective Planes 1
Affine Planes 6
Subplanes of a Plane 9
Exercises 12
chapter 2. COORDINATIZATION OF A PROJECTIVE PLANE:
TERNARY RINGS 13
Coordinatization of Projective Planes 13
Coordinatization of Af fine Planes 18
Quasifields 18
Duality and Coordinates 22
Exercises 22
chapter 3. PERMUTATION GROUPS 24
Burnside s Theorems 27
Transitivity 29
Primitivity 31
Frobenius Groups 35
Exercises 36
chapter 4. COLLINEATIONS AND PERSPECnVITIES 37
Collineations of Planes 37
Collineations as Permutations 40
Perspectivities 44
viii CONTENTS
Involutory Collineations 47
Perspectivities in Collineation Groups 50
Exercises 51
chapter 5. PERSPECnvmES AND TERNARY RINGS 53
(P, 0 Transitivity 53
(/ , C) Transitivity and Coordinatization 56
Desargues Configuration 63
Exercises 66
chapter 6. TRANSLATION PLANES AND DUAL
TRANSLATION PLANES 69
Translation Planes 69
Dual Translation Planes 75
The Brack Bose Representation 78
Exercises 78
chapter 7. DERIVABILITY 79
The Theory of Derivation 79
Derivability and Dual Translation Planes 83
Some Informative Remarks 87
chapter 8. THREE SPECIAL EXAMPLES 88
Exercises 97
chapter 9. HISTORICAL INTERLUDE 98
Historical Outline 99
chapter 10. ANDRE S THEOREM 102
chapter 11. FINITE AFFINE LINE TRANSITIVE
COLLINEATION GROUPS 105
Exercises 111
chapter 12. BLOCK ORBITS 112
Three Useful Lemmas 112
Block Orbits 113
Strong Block Orbits 117
Exercises 119
chapter 13. BLOCK ORBITS AND TRANSLATION
PLANES 120
Exercises 124
chapter 14. RANK (r,s) COLLINEATION GROUPS 125
chapter 15. COLLINEATION GROUPS PRIMITIVE ON
AFFINE POINTS 135
CONTENTS ix
chapter 16. ADDITIONAL COMMENTS 140
Transitivity on Affine Quadrangles 140
Unsolved Questions 143
Transitive Projective Planes 146
Bibliography 149
Index 153
|
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| dewey-search | 516.4 |
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| discipline | Mathematik |
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| genre | Transitive Kollineationsgruppe gnd |
| genre_facet | Transitive Kollineationsgruppe |
| id | DE-604.BV000072150 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T15:08:08Z |
| institution | BVB |
| isbn | 0444006206 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000031708 |
| oclc_num | 7577781 |
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| owner_facet | DE-12 DE-91G DE-BY-TUM DE-384 DE-703 DE-739 DE-188 |
| physical | XII, 155 S. graph. Darst. |
| publishDate | 1982 |
| publishDateSearch | 1982 |
| publishDateSort | 1982 |
| publisher | North Holland |
| record_format | marc |
| spelling | Kallaher, Michael J. Verfasser aut Affine planes with transitive collineation groups New York u.a. North Holland 1982 XII, 155 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Collineation Geometry, Affine Kollineation (DE-588)4164692-7 gnd rswk-swf Affine Ebene (DE-588)4141564-4 gnd rswk-swf Transitive Kollineationsgruppe gnd rswk-swf Affine Ebene (DE-588)4141564-4 s Transitive Kollineationsgruppe f DE-604 Kollineation (DE-588)4164692-7 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000031708&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kallaher, Michael J. Affine planes with transitive collineation groups Collineation Geometry, Affine Kollineation (DE-588)4164692-7 gnd Affine Ebene (DE-588)4141564-4 gnd |
| subject_GND | (DE-588)4164692-7 (DE-588)4141564-4 |
| title | Affine planes with transitive collineation groups |
| title_auth | Affine planes with transitive collineation groups |
| title_exact_search | Affine planes with transitive collineation groups |
| title_full | Affine planes with transitive collineation groups |
| title_fullStr | Affine planes with transitive collineation groups |
| title_full_unstemmed | Affine planes with transitive collineation groups |
| title_short | Affine planes with transitive collineation groups |
| title_sort | affine planes with transitive collineation groups |
| topic | Collineation Geometry, Affine Kollineation (DE-588)4164692-7 gnd Affine Ebene (DE-588)4141564-4 gnd |
| topic_facet | Collineation Geometry, Affine Kollineation Affine Ebene Transitive Kollineationsgruppe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000031708&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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