Sporadic groups:
Sporadic Groups is the first step in a programme to provide a uniform, self-contained treatment of the foundational material on the sporadic finite simple groups. The classification of the finite simple groups is one of the premier achievements of modern mathematics. The classification demonstrates...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
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Cambridge
Cambridge University Press
1994
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| Schriftenreihe: | Cambridge tracts in mathematics
104 |
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| Online-Zugang: | BSB01 FHN01 UBR01 Volltext |
| Zusammenfassung: | Sporadic Groups is the first step in a programme to provide a uniform, self-contained treatment of the foundational material on the sporadic finite simple groups. The classification of the finite simple groups is one of the premier achievements of modern mathematics. The classification demonstrates that each finite simple group is either a finite analogue of a simple Lie group or one of 26 pathological sporadic groups. Sporadic Groups provides for the first time a self-contained treatment of the foundations of the theory of sporadic groups accessible to mathematicians with a basic background in finite groups such as in the author's text Finite Group Theory. Introductory material useful for studying the sporadics, such as a discussion of large extraspecial 2-subgroups and Tits' coset geometries, opens the book. A construction of the Mathieu groups as the automorphism groups of Steiner systems follows. The Golay and Todd modules, and the 2-local geometry for M24 are discussed. This is followed by the standard construction of Conway of the Leech lattice and the Conway group. The Monster is constructed as the automorphism group of the Griess algebra using some of the best features of the approaches of Griess, Conway, and Tits, plus a few new wrinkles. Researchers in finite group theory will find this text invaluable. The subjects treated will interest combinatorists, number theorists, and conformal field theorists |
| Beschreibung: | 1 Online-Ressource (xii, 314 Seiten) |
| ISBN: | 9780511665585 |
| DOI: | 10.1017/CBO9780511665585 |
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| 505 | 8 | |a 1. Preliminary Results -- 2. 2-Structure in Finite Groups -- 3. Algebras, Codes, and Forms -- 4. Symplectic 2-Loops -- 5. The Discovery, Existence, and Uniqueness of the Sporadics -- 6. The Mathieu Groups, Their Steiner Systems, and the Golay Code -- 7. The Geometry and Structure of M[subscript 24] -- 8. The Conway Groups and the Leech Lattice -- 9. Subgroups of [actual symbol not reproducible] -- 10. The Griess Algebra and the Monster -- 11. Subgroups of Groups of Monster Type -- 12. Coverings of Graphs and Simplicial Complexes -- 13. The Geometry of Amalgams -- 14. The Uniqueness of Groups of Type M[subscript 24], He, and L[subscript 5](2) -- 15. The Group U[subscript 4](3) -- 16. Groups of Conway, Suzuki, and Hall-Janko Type -- 17. Subgroups of Prime Order in Five Sporadic Groups | |
| 520 | |a Sporadic Groups is the first step in a programme to provide a uniform, self-contained treatment of the foundational material on the sporadic finite simple groups. The classification of the finite simple groups is one of the premier achievements of modern mathematics. The classification demonstrates that each finite simple group is either a finite analogue of a simple Lie group or one of 26 pathological sporadic groups. Sporadic Groups provides for the first time a self-contained treatment of the foundations of the theory of sporadic groups accessible to mathematicians with a basic background in finite groups such as in the author's text Finite Group Theory. Introductory material useful for studying the sporadics, such as a discussion of large extraspecial 2-subgroups and Tits' coset geometries, opens the book. A construction of the Mathieu groups as the automorphism groups of Steiner systems follows. The Golay and Todd modules, and the 2-local geometry for M24 are discussed. This is followed by the standard construction of Conway of the Leech lattice and the Conway group. The Monster is constructed as the automorphism group of the Griess algebra using some of the best features of the approaches of Griess, Conway, and Tits, plus a few new wrinkles. Researchers in finite group theory will find this text invaluable. The subjects treated will interest combinatorists, number theorists, and conformal field theorists | ||
| 650 | 4 | |a Sporadic groups (Mathematics) | |
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Datensatz im Suchindex
| _version_ | 1804176884846559232 |
|---|---|
| any_adam_object | |
| author | Aschbacher, Michael 1944- |
| author_GND | (DE-588)142400955 |
| author_facet | Aschbacher, Michael 1944- |
| author_role | aut |
| author_sort | Aschbacher, Michael 1944- |
| author_variant | m a ma |
| building | Verbundindex |
| bvnumber | BV043942252 |
| classification_rvk | SK 260 |
| collection | ZDB-20-CBO |
| contents | 1. Preliminary Results -- 2. 2-Structure in Finite Groups -- 3. Algebras, Codes, and Forms -- 4. Symplectic 2-Loops -- 5. The Discovery, Existence, and Uniqueness of the Sporadics -- 6. The Mathieu Groups, Their Steiner Systems, and the Golay Code -- 7. The Geometry and Structure of M[subscript 24] -- 8. The Conway Groups and the Leech Lattice -- 9. Subgroups of [actual symbol not reproducible] -- 10. The Griess Algebra and the Monster -- 11. Subgroups of Groups of Monster Type -- 12. Coverings of Graphs and Simplicial Complexes -- 13. The Geometry of Amalgams -- 14. The Uniqueness of Groups of Type M[subscript 24], He, and L[subscript 5](2) -- 15. The Group U[subscript 4](3) -- 16. Groups of Conway, Suzuki, and Hall-Janko Type -- 17. Subgroups of Prime Order in Five Sporadic Groups |
| ctrlnum | (ZDB-20-CBO)CR9780511665585 (OCoLC)849941471 (DE-599)BVBBV043942252 |
| dewey-full | 512/.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.2 |
| dewey-search | 512/.2 |
| dewey-sort | 3512 12 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9780511665585 |
| format | Electronic eBook |
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| id | DE-604.BV043942252 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:17Z |
| institution | BVB |
| isbn | 9780511665585 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029351221 |
| oclc_num | 849941471 |
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| physical | 1 Online-Ressource (xii, 314 Seiten) |
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| publishDate | 1994 |
| publishDateSearch | 1994 |
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| publisher | Cambridge University Press |
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| spelling | Aschbacher, Michael 1944- Verfasser (DE-588)142400955 aut Sporadic groups Michael Aschbacher Cambridge Cambridge University Press 1994 1 Online-Ressource (xii, 314 Seiten) txt rdacontent c rdamedia cr rdacarrier Cambridge tracts in mathematics 104 1. Preliminary Results -- 2. 2-Structure in Finite Groups -- 3. Algebras, Codes, and Forms -- 4. Symplectic 2-Loops -- 5. The Discovery, Existence, and Uniqueness of the Sporadics -- 6. The Mathieu Groups, Their Steiner Systems, and the Golay Code -- 7. The Geometry and Structure of M[subscript 24] -- 8. The Conway Groups and the Leech Lattice -- 9. Subgroups of [actual symbol not reproducible] -- 10. The Griess Algebra and the Monster -- 11. Subgroups of Groups of Monster Type -- 12. Coverings of Graphs and Simplicial Complexes -- 13. The Geometry of Amalgams -- 14. The Uniqueness of Groups of Type M[subscript 24], He, and L[subscript 5](2) -- 15. The Group U[subscript 4](3) -- 16. Groups of Conway, Suzuki, and Hall-Janko Type -- 17. Subgroups of Prime Order in Five Sporadic Groups Sporadic Groups is the first step in a programme to provide a uniform, self-contained treatment of the foundational material on the sporadic finite simple groups. The classification of the finite simple groups is one of the premier achievements of modern mathematics. The classification demonstrates that each finite simple group is either a finite analogue of a simple Lie group or one of 26 pathological sporadic groups. Sporadic Groups provides for the first time a self-contained treatment of the foundations of the theory of sporadic groups accessible to mathematicians with a basic background in finite groups such as in the author's text Finite Group Theory. Introductory material useful for studying the sporadics, such as a discussion of large extraspecial 2-subgroups and Tits' coset geometries, opens the book. A construction of the Mathieu groups as the automorphism groups of Steiner systems follows. The Golay and Todd modules, and the 2-local geometry for M24 are discussed. This is followed by the standard construction of Conway of the Leech lattice and the Conway group. The Monster is constructed as the automorphism group of the Griess algebra using some of the best features of the approaches of Griess, Conway, and Tits, plus a few new wrinkles. Researchers in finite group theory will find this text invaluable. The subjects treated will interest combinatorists, number theorists, and conformal field theorists Sporadic groups (Mathematics) Sporadische Gruppe (DE-588)4389412-4 gnd rswk-swf Gruppe Mathematik (DE-588)4022379-6 gnd rswk-swf Sporadische Gruppe (DE-588)4389412-4 s DE-604 Gruppe Mathematik (DE-588)4022379-6 s Erscheint auch als Druck-Ausgabe 978-0-521-42049-5 Erscheint auch als Druck-Ausgabe 978-0-521-05686-1 https://doi.org/10.1017/CBO9780511665585 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Aschbacher, Michael 1944- Sporadic groups 1. Preliminary Results -- 2. 2-Structure in Finite Groups -- 3. Algebras, Codes, and Forms -- 4. Symplectic 2-Loops -- 5. The Discovery, Existence, and Uniqueness of the Sporadics -- 6. The Mathieu Groups, Their Steiner Systems, and the Golay Code -- 7. The Geometry and Structure of M[subscript 24] -- 8. The Conway Groups and the Leech Lattice -- 9. Subgroups of [actual symbol not reproducible] -- 10. The Griess Algebra and the Monster -- 11. Subgroups of Groups of Monster Type -- 12. Coverings of Graphs and Simplicial Complexes -- 13. The Geometry of Amalgams -- 14. The Uniqueness of Groups of Type M[subscript 24], He, and L[subscript 5](2) -- 15. The Group U[subscript 4](3) -- 16. Groups of Conway, Suzuki, and Hall-Janko Type -- 17. Subgroups of Prime Order in Five Sporadic Groups Sporadic groups (Mathematics) Sporadische Gruppe (DE-588)4389412-4 gnd Gruppe Mathematik (DE-588)4022379-6 gnd |
| subject_GND | (DE-588)4389412-4 (DE-588)4022379-6 |
| title | Sporadic groups |
| title_auth | Sporadic groups |
| title_exact_search | Sporadic groups |
| title_full | Sporadic groups Michael Aschbacher |
| title_fullStr | Sporadic groups Michael Aschbacher |
| title_full_unstemmed | Sporadic groups Michael Aschbacher |
| title_short | Sporadic groups |
| title_sort | sporadic groups |
| topic | Sporadic groups (Mathematics) Sporadische Gruppe (DE-588)4389412-4 gnd Gruppe Mathematik (DE-588)4022379-6 gnd |
| topic_facet | Sporadic groups (Mathematics) Sporadische Gruppe Gruppe Mathematik |
| url | https://doi.org/10.1017/CBO9780511665585 |
| work_keys_str_mv | AT aschbachermichael sporadicgroups |