3-transposition groups:
In 1970 Bernd Fischer proved his beautiful theorem classifying the almost simple groups generated by 3-transpositions, and in the process discovered three new sporadic groups, now known as the Fischer groups. Since then, the theory of 3-transposition groups has become an important part of finite sim...
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| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
1997
|
| Series: | Cambridge tracts in mathematics
124 |
| Subjects: | |
| Online Access: | BSB01 FHN01 UBR01 Volltext |
| Summary: | In 1970 Bernd Fischer proved his beautiful theorem classifying the almost simple groups generated by 3-transpositions, and in the process discovered three new sporadic groups, now known as the Fischer groups. Since then, the theory of 3-transposition groups has become an important part of finite simple group theory, but Fischer's work has remained unpublished. 3-Transposition Groups contains the first published proof of Fischer's Theorem, written out completely in one place. Fischer's result, while important and deep (covering a number of complex examples), can be understood by any student with some knowledge of elementary group theory and finite geometry. Thus Part I has minimal prerequisites and could be used as a text for an intermediate level graduate course. Parts II and III are aimed at specialists in finite groups and are a step in the author's program to supply a strong foundation for the theory of sporadic groups |
| Physical Description: | 1 Online-Ressource (vii, 260 Seiten) |
| ISBN: | 9780511759413 |
| DOI: | 10.1017/CBO9780511759413 |
Staff View
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| 505 | 8 | |a pt. I. Fischer's Theory. 1. Preliminaries. 2. Commuting graphs of groups. 3. The structure of 3-transposition groups. 4. Classical groups generated by 3-transpositions. 5. Fischer's Theorem. 6. The geometry of 3-transposition groups -- pt. II. The existence and uniqueness of the Fischer groups. 7. Some group extensions. 8. Almost 3-transposition groups. 9. Uniqueness systems and coverings of graphs. 10. U[subscript 4](3) as a subgroup of U[subscript 6](2). 11. The existence and uniqueness of the Fischer groups -- pt. III. The local structure of the Fischer groups. 12. The 2-local structure of the Fischer groups. 13. Elements of order 3 in orthogonal groups over GF(3). 14. Odd locals in Fischer groups. 15. Normalizers of subgroups of prime order in Fischer groups | |
| 520 | |a In 1970 Bernd Fischer proved his beautiful theorem classifying the almost simple groups generated by 3-transpositions, and in the process discovered three new sporadic groups, now known as the Fischer groups. Since then, the theory of 3-transposition groups has become an important part of finite simple group theory, but Fischer's work has remained unpublished. 3-Transposition Groups contains the first published proof of Fischer's Theorem, written out completely in one place. Fischer's result, while important and deep (covering a number of complex examples), can be understood by any student with some knowledge of elementary group theory and finite geometry. Thus Part I has minimal prerequisites and could be used as a text for an intermediate level graduate course. Parts II and III are aimed at specialists in finite groups and are a step in the author's program to supply a strong foundation for the theory of sporadic groups | ||
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Record in the Search Index
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| contents | pt. I. Fischer's Theory. 1. Preliminaries. 2. Commuting graphs of groups. 3. The structure of 3-transposition groups. 4. Classical groups generated by 3-transpositions. 5. Fischer's Theorem. 6. The geometry of 3-transposition groups -- pt. II. The existence and uniqueness of the Fischer groups. 7. Some group extensions. 8. Almost 3-transposition groups. 9. Uniqueness systems and coverings of graphs. 10. U[subscript 4](3) as a subgroup of U[subscript 6](2). 11. The existence and uniqueness of the Fischer groups -- pt. III. The local structure of the Fischer groups. 12. The 2-local structure of the Fischer groups. 13. Elements of order 3 in orthogonal groups over GF(3). 14. Odd locals in Fischer groups. 15. Normalizers of subgroups of prime order in Fischer groups |
| ctrlnum | (ZDB-20-CBO)CR9780511759413 (OCoLC)849911068 (DE-599)BVBBV043942266 |
| dewey-full | 512.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
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| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9780511759413 |
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| id | DE-604.BV043942266 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:17Z |
| institution | BVB |
| isbn | 9780511759413 |
| language | English |
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| publishDate | 1997 |
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| spelling | Aschbacher, Michael 1944- Verfasser (DE-588)142400955 aut 3-transposition groups Michael Aschbacher Cambridge Cambridge University Press 1997 1 Online-Ressource (vii, 260 Seiten) txt rdacontent c rdamedia cr rdacarrier Cambridge tracts in mathematics 124 pt. I. Fischer's Theory. 1. Preliminaries. 2. Commuting graphs of groups. 3. The structure of 3-transposition groups. 4. Classical groups generated by 3-transpositions. 5. Fischer's Theorem. 6. The geometry of 3-transposition groups -- pt. II. The existence and uniqueness of the Fischer groups. 7. Some group extensions. 8. Almost 3-transposition groups. 9. Uniqueness systems and coverings of graphs. 10. U[subscript 4](3) as a subgroup of U[subscript 6](2). 11. The existence and uniqueness of the Fischer groups -- pt. III. The local structure of the Fischer groups. 12. The 2-local structure of the Fischer groups. 13. Elements of order 3 in orthogonal groups over GF(3). 14. Odd locals in Fischer groups. 15. Normalizers of subgroups of prime order in Fischer groups In 1970 Bernd Fischer proved his beautiful theorem classifying the almost simple groups generated by 3-transpositions, and in the process discovered three new sporadic groups, now known as the Fischer groups. Since then, the theory of 3-transposition groups has become an important part of finite simple group theory, but Fischer's work has remained unpublished. 3-Transposition Groups contains the first published proof of Fischer's Theorem, written out completely in one place. Fischer's result, while important and deep (covering a number of complex examples), can be understood by any student with some knowledge of elementary group theory and finite geometry. Thus Part I has minimal prerequisites and could be used as a text for an intermediate level graduate course. Parts II and III are aimed at specialists in finite groups and are a step in the author's program to supply a strong foundation for the theory of sporadic groups Finite groups Endliche einfache Gruppe (DE-588)4123136-3 gnd rswk-swf Endliche einfache Gruppe (DE-588)4123136-3 s DE-604 Erscheint auch als Druck-Ausgabe 978-0-521-10102-8 Erscheint auch als Druck-Ausgabe 978-0-521-57196-8 https://doi.org/10.1017/CBO9780511759413 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Aschbacher, Michael 1944- 3-transposition groups pt. I. Fischer's Theory. 1. Preliminaries. 2. Commuting graphs of groups. 3. The structure of 3-transposition groups. 4. Classical groups generated by 3-transpositions. 5. Fischer's Theorem. 6. The geometry of 3-transposition groups -- pt. II. The existence and uniqueness of the Fischer groups. 7. Some group extensions. 8. Almost 3-transposition groups. 9. Uniqueness systems and coverings of graphs. 10. U[subscript 4](3) as a subgroup of U[subscript 6](2). 11. The existence and uniqueness of the Fischer groups -- pt. III. The local structure of the Fischer groups. 12. The 2-local structure of the Fischer groups. 13. Elements of order 3 in orthogonal groups over GF(3). 14. Odd locals in Fischer groups. 15. Normalizers of subgroups of prime order in Fischer groups Finite groups Endliche einfache Gruppe (DE-588)4123136-3 gnd |
| subject_GND | (DE-588)4123136-3 |
| title | 3-transposition groups |
| title_auth | 3-transposition groups |
| title_exact_search | 3-transposition groups |
| title_full | 3-transposition groups Michael Aschbacher |
| title_fullStr | 3-transposition groups Michael Aschbacher |
| title_full_unstemmed | 3-transposition groups Michael Aschbacher |
| title_short | 3-transposition groups |
| title_sort | 3 transposition groups |
| topic | Finite groups Endliche einfache Gruppe (DE-588)4123136-3 gnd |
| topic_facet | Finite groups Endliche einfache Gruppe |
| url | https://doi.org/10.1017/CBO9780511759413 |
| work_keys_str_mv | AT aschbachermichael 3transpositiongroups |