A survey of binary systems:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin u.a.
Springer
1971
|
| Ausgabe: | 3. print., corr. |
| Schriftenreihe: | Ergebnisse der Mathematik und ihrer Grenzgebiete
20 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 163 - 181 |
| Beschreibung: | VIII, 186 S. |
| ISBN: | 3540034978 0387034978 |
Internformat
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| 245 | 1 | 0 | |a A survey of binary systems |c Richard Hubert Bruck |
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| 264 | 1 | |a Berlin u.a. |b Springer |c 1971 | |
| 300 | |a VIII, 186 S. | ||
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| 490 | 1 | |a Ergebnisse der Mathematik und ihrer Grenzgebiete |v 20 | |
| 500 | |a Literaturverz. S. 163 - 181 | ||
| 650 | 4 | |a Algebra, Abstract | |
| 650 | 4 | |a Binary system (Mathematics) | |
| 650 | 4 | |a Group theory | |
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Datensatz im Suchindex
| _version_ | 1804117026131673088 |
|---|---|
| adam_text | Contents
I. Systems and their Generation 1
1. Groupoids 1
2. Quasigroups 8
3. Loops 15
4. Loops, nets and projective planes 17
5. General algebras 21
II. The Associative Law 23
1. Semigroups 23
2. Cancellation semigroups 26
3. Groups 28
4. Homomorphic imbedding 32
5. Brandt groupoids. Mixed groups 34
6. Polyadic groups. Flocks 36
7. Multigroups, hypergroups, etc 41
8. Ideal structure of semigroups 44
9. Multiplication semigroups 53
III. Isotopy 56
1. Isotopy of groupoids 56
2. Invariants of principal isotopy 57
3. Non-invariants of principal isotopy 58
4. Isotopy and geometry 59
IV. Homomorphism Theory of Loops 60
1. Normal subloops 60
2. Loops with operators 65
3. The refinement theorem 67
4. Normal endomorphisms 68
5. Direct decomposition 72
6. Characteristic free factors 86
7. Hamiltonian loops 87
8. Loops with transitive automorphism groups 88
9. Homomorphism theory of quasigroups 90
10. Homomorphism theory of other systems 91
V. Lagrange s Theorem for Loops 92
1. Coset expansion 92
2. Lagrange theorems 92
VI. Nilpotency of Loops 94
1. A general theory of nilpotency 94
2. The Frattini subloop 97
3. Hall s enumeration principle 99
4. Local properties 102
5. Ordered loops 108
VII. Moufang Loops 110
1. Groupoids with the inverse property 110
2. Moufang elements 112
3. Moufang loops 115
4. Moufang s theorem 117
5. The core 120
VIII Contents
VIII. Commutative Moufang Loops 130
1. Examples 130
2. Two and three generators 132
3. Four generators 133
4. A calculus of associator subloops 138
5. The distributor 141
6. Five generators 143
7. The functions / 148
8. Two lemmas 149
9. The sets £ («) 150
10. The main theorem 151
11. Local properties 157
Bibliography 163
A. Books 163
B. Selected papers 164
C. The Main Bibliography 164
I. Algebras (General) 164
II. Groupoids 166
III. Loops and Quasigroups 166
IV. Multigroups 169
V. Semigroups 170
VI. Other Associative Systems 177
D. Supplement 178
Recent papers on Group Axioms 178
Algebras (General) 178
Groupoids 178
Loops and Quasigroups 178
Multigroups 179
Semigroups 179
Index 182
Contents
I. Systems and their Generation 1
1. Groupoids 1
2. Quasigroups 8
3. Loops 15
4. Loops, nets and projective planes 17
5. General algebras 21
II. The Associative Law 23
1. Semigroups 23
2. Cancellation semigroups 26
3. Groups 28
4. Homomorphic imbedding 32
5. Brandt groupoids. Mixed groups 34
6. Polyadic groups. Flocks 36
7. Multigroups, hypergroups, etc 41
8. Ideal structure of semigroups 44
9. Multiplication semigroups 53
III. Isotopy 56
1. Isotopy of groupoids 56
2. Invariants of principal isotopy 57
3. Non invariants of principal isotopy 58
4. Isotopy and geometry 59
IV. Homomorphism Theory of Loops 60
1. Normal subloops 60
2. Loops with operators 65
3. The refinement theorem 67
4. Normal endomorphisms 68
5. Direct decomposition 72
6. Characteristic free factors 86
7. Hamiltonian loops 87
8. Loops with transitive automorphism groups 88
9. Homomorphism theory of quasigroups 90
10. Homomorphism theory of other systems 91
V. Lagrange s Theorem for Loops 92
1. Coset expansion 92
2. Lagrange theorems 92
VI. Nilpotency of Loops 94
1. A general theory of nilpotency 94
2. The Frattini subloop 97
3. Hall s enumeration principle 99
4. Local properties 102
5. Ordered loops 108
VII. Moufang Loops 110
1. Groupoids with the inverse property 110
2. Moufang elements 112
3. Moufang loops 115
4. Moufang s theorem 117
5. The core 120
VIII Contents
VIII. Commutative Moufang Loops 130
1. Examples 130
2. Two and three generators 132
3. Four generators 133
4. A calculus of associator subloops 138
5. The distributor 141
6. Five generators 143
7. The functions / 148
8. Two lemmas 149
9. The sets £ («) 150
10. The main theorem 151
11. Local properties 157
Bibliography 163
A. Books 163
B. Selected papers 164
C. The Main Bibliography 164
I. Algebras (General) 164
II. Groupoids 166
III. Loops and Quasigroups 166
IV. Multigroups 169
V. Semigroups 170
VI. Other Associative Systems 177
D. Supplement 178
Recent papers on Group Axioms 178
Algebras (General) 178
Groupoids 178
Loops and Quasigroups 178
Multigroups 179
Semigroups 179
Index 182
|
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| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.74 |
| dewey-search | 512/.74 |
| dewey-sort | 3512 274 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 3. print., corr. |
| format | Book |
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| id | DE-604.BV002646137 |
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| indexdate | 2024-07-09T15:47:51Z |
| institution | BVB |
| isbn | 3540034978 0387034978 |
| language | English |
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| physical | VIII, 186 S. |
| psigel | HUB-ZB011200710 |
| publishDate | 1971 |
| publishDateSearch | 1971 |
| publishDateSort | 1971 |
| publisher | Springer |
| record_format | marc |
| series | Ergebnisse der Mathematik und ihrer Grenzgebiete |
| series2 | Ergebnisse der Mathematik und ihrer Grenzgebiete |
| spelling | Bruck, Richard Hubert Verfasser aut A survey of binary systems Richard Hubert Bruck 3. print., corr. Berlin u.a. Springer 1971 VIII, 186 S. txt rdacontent n rdamedia nc rdacarrier Ergebnisse der Mathematik und ihrer Grenzgebiete 20 Literaturverz. S. 163 - 181 Algebra, Abstract Binary system (Mathematics) Group theory Gruppentheorie (DE-588)4072157-7 gnd rswk-swf Dualsystem (DE-588)4150805-1 gnd rswk-swf Gruppentheorie (DE-588)4072157-7 s Dualsystem (DE-588)4150805-1 s 1\p DE-604 DE-604 Ergebnisse der Mathematik und ihrer Grenzgebiete 20 (DE-604)BV005871160 20 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001697863&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001697863&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Bruck, Richard Hubert A survey of binary systems Ergebnisse der Mathematik und ihrer Grenzgebiete Algebra, Abstract Binary system (Mathematics) Group theory Gruppentheorie (DE-588)4072157-7 gnd Dualsystem (DE-588)4150805-1 gnd |
| subject_GND | (DE-588)4072157-7 (DE-588)4150805-1 |
| title | A survey of binary systems |
| title_auth | A survey of binary systems |
| title_exact_search | A survey of binary systems |
| title_full | A survey of binary systems Richard Hubert Bruck |
| title_fullStr | A survey of binary systems Richard Hubert Bruck |
| title_full_unstemmed | A survey of binary systems Richard Hubert Bruck |
| title_short | A survey of binary systems |
| title_sort | a survey of binary systems |
| topic | Algebra, Abstract Binary system (Mathematics) Group theory Gruppentheorie (DE-588)4072157-7 gnd Dualsystem (DE-588)4150805-1 gnd |
| topic_facet | Algebra, Abstract Binary system (Mathematics) Group theory Gruppentheorie Dualsystem |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001697863&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001697863&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV005871160 |
| work_keys_str_mv | AT bruckrichardhubert asurveyofbinarysystems |
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