Local analysis for the odd order theorem:
In 1963 Walter Feit and John G. Thompson published a proof of a 1911 conjecture by Burnside that every finite group of odd order is solvable. This proof, which ran for 255 pages, was a tour-de-force of mathematics and inspired intense effort to classify finite simple groups. This book presents a rev...
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | Englisch |
| Veröffentlicht: |
Cambridge
Cambridge University Press
1994
|
| Schriftenreihe: | London Mathematical Society lecture note series
188 |
| Schlagwörter: | |
| Links: | https://doi.org/10.1017/CBO9780511665592 https://doi.org/10.1017/CBO9780511665592 https://doi.org/10.1017/CBO9780511665592 |
| Zusammenfassung: | In 1963 Walter Feit and John G. Thompson published a proof of a 1911 conjecture by Burnside that every finite group of odd order is solvable. This proof, which ran for 255 pages, was a tour-de-force of mathematics and inspired intense effort to classify finite simple groups. This book presents a revision and expansion of the first half of the proof of the Feit–Thompson theorem. Simpler, more detailed proofs are provided for some intermediate theorems. Recent results are used to shorten other proofs. The book will make the first half of this remarkable proof accessible to readers familiar with just the rudiments of group theory |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Umfang: | 1 online resource (xi, 174 pages) |
| ISBN: | 9780511665592 |
| DOI: | 10.1017/CBO9780511665592 |
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| 100 | 1 | |a Bender, Helmut |d 1942- |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Local analysis for the odd order theorem |c Helmut Bender and George Glauberman, with the assistance of Walter Carlip |
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| 500 | |a Title from publisher's bibliographic system (viewed on 05 Oct 2015) | ||
| 505 | 8 | |a Ch. I. Preliminary Results. 1. Elementary Properties of Solvable Groups. 2. General Results on Representations. 3. Actions of Frobenius Groups and Related Results. 4. p-Groups of Small Rank. 5. Narrow p-Groups. 6. Additional Results -- Ch. II. The Uniqueness Theorem. 7. The Transitivity Theorem. 8. The Fitting Subgroup of a Maximal Subgroup. 9. The Uniqueness Theorem -- Ch. III. Maximal Subgroups. 10. The Subgroups M[subscript [alpha]] and A[subscript [sigma]]. 11. Exceptional Maximal Subgroups. 12. The Subgroup E. 13. Prime Action -- Ch. IV. The Family of All Maximal Subgroups of G. 14. Maximal Subgroups of Type [actual symbol not reproducible] and Counting Arguments. 15. The Subgroup M[subscript F]. 16. The Main Results -- App. A: Prerequisites and p-Stability -- App. B: The Puig Subgroup -- App. C: The Final Contradiction -- App. D: CN-Groups of Odd Order -- App. E: Further Results of Feit and Thompson | |
| 520 | |a In 1963 Walter Feit and John G. Thompson published a proof of a 1911 conjecture by Burnside that every finite group of odd order is solvable. This proof, which ran for 255 pages, was a tour-de-force of mathematics and inspired intense effort to classify finite simple groups. This book presents a revision and expansion of the first half of the proof of the Feit–Thompson theorem. Simpler, more detailed proofs are provided for some intermediate theorems. Recent results are used to shorten other proofs. The book will make the first half of this remarkable proof accessible to readers familiar with just the rudiments of group theory | ||
| 650 | 4 | |a Feit-Thompson theorem | |
| 650 | 4 | |a Solvable groups | |
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| 700 | 1 | |a Carlip, Walter |d 1956- |e Sonstige |4 oth | |
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Datensatz im Suchindex
| _version_ | 1818982568551251968 |
|---|---|
| any_adam_object | |
| author | Bender, Helmut 1942- |
| author_facet | Bender, Helmut 1942- |
| author_role | aut |
| author_sort | Bender, Helmut 1942- |
| author_variant | h b hb |
| building | Verbundindex |
| bvnumber | BV043941768 |
| classification_rvk | SI 320 SK 260 ST 260 |
| collection | ZDB-20-CBO |
| contents | Ch. I. Preliminary Results. 1. Elementary Properties of Solvable Groups. 2. General Results on Representations. 3. Actions of Frobenius Groups and Related Results. 4. p-Groups of Small Rank. 5. Narrow p-Groups. 6. Additional Results -- Ch. II. The Uniqueness Theorem. 7. The Transitivity Theorem. 8. The Fitting Subgroup of a Maximal Subgroup. 9. The Uniqueness Theorem -- Ch. III. Maximal Subgroups. 10. The Subgroups M[subscript [alpha]] and A[subscript [sigma]]. 11. Exceptional Maximal Subgroups. 12. The Subgroup E. 13. Prime Action -- Ch. IV. The Family of All Maximal Subgroups of G. 14. Maximal Subgroups of Type [actual symbol not reproducible] and Counting Arguments. 15. The Subgroup M[subscript F]. 16. The Main Results -- App. A: Prerequisites and p-Stability -- App. B: The Puig Subgroup -- App. C: The Final Contradiction -- App. D: CN-Groups of Odd Order -- App. E: Further Results of Feit and Thompson |
| ctrlnum | (ZDB-20-CBO)CR9780511665592 (OCoLC)849903340 (DE-599)BVBBV043941768 |
| 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 | Informatik Mathematik |
| doi_str_mv | 10.1017/CBO9780511665592 |
| format | Electronic eBook |
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| id | DE-604.BV043941768 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T17:49:17Z |
| institution | BVB |
| isbn | 9780511665592 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029350738 |
| oclc_num | 849903340 |
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| owner | DE-12 DE-92 |
| owner_facet | DE-12 DE-92 |
| physical | 1 online resource (xi, 174 pages) |
| psigel | ZDB-20-CBO ZDB-20-CBO BSB_PDA_CBO ZDB-20-CBO FHN_PDA_CBO |
| publishDate | 1994 |
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| publisher | Cambridge University Press |
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| spelling | Bender, Helmut 1942- Verfasser aut Local analysis for the odd order theorem Helmut Bender and George Glauberman, with the assistance of Walter Carlip Cambridge Cambridge University Press 1994 1 online resource (xi, 174 pages) txt rdacontent c rdamedia cr rdacarrier London Mathematical Society lecture note series 188 Title from publisher's bibliographic system (viewed on 05 Oct 2015) Ch. I. Preliminary Results. 1. Elementary Properties of Solvable Groups. 2. General Results on Representations. 3. Actions of Frobenius Groups and Related Results. 4. p-Groups of Small Rank. 5. Narrow p-Groups. 6. Additional Results -- Ch. II. The Uniqueness Theorem. 7. The Transitivity Theorem. 8. The Fitting Subgroup of a Maximal Subgroup. 9. The Uniqueness Theorem -- Ch. III. Maximal Subgroups. 10. The Subgroups M[subscript [alpha]] and A[subscript [sigma]]. 11. Exceptional Maximal Subgroups. 12. The Subgroup E. 13. Prime Action -- Ch. IV. The Family of All Maximal Subgroups of G. 14. Maximal Subgroups of Type [actual symbol not reproducible] and Counting Arguments. 15. The Subgroup M[subscript F]. 16. The Main Results -- App. A: Prerequisites and p-Stability -- App. B: The Puig Subgroup -- App. C: The Final Contradiction -- App. D: CN-Groups of Odd Order -- App. E: Further Results of Feit and Thompson In 1963 Walter Feit and John G. Thompson published a proof of a 1911 conjecture by Burnside that every finite group of odd order is solvable. This proof, which ran for 255 pages, was a tour-de-force of mathematics and inspired intense effort to classify finite simple groups. This book presents a revision and expansion of the first half of the proof of the Feit–Thompson theorem. Simpler, more detailed proofs are provided for some intermediate theorems. Recent results are used to shorten other proofs. The book will make the first half of this remarkable proof accessible to readers familiar with just the rudiments of group theory Feit-Thompson theorem Solvable groups p-Gruppe (DE-588)4174108-0 gnd rswk-swf Endliche Gruppe (DE-588)4014651-0 gnd rswk-swf Endliche Gruppe (DE-588)4014651-0 s p-Gruppe (DE-588)4174108-0 s 1\p DE-604 Glauberman, G. 1941- Sonstige oth Carlip, Walter 1956- Sonstige oth Erscheint auch als Druckausgabe 978-0-521-45716-3 https://doi.org/10.1017/CBO9780511665592 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Bender, Helmut 1942- Local analysis for the odd order theorem Ch. I. Preliminary Results. 1. Elementary Properties of Solvable Groups. 2. General Results on Representations. 3. Actions of Frobenius Groups and Related Results. 4. p-Groups of Small Rank. 5. Narrow p-Groups. 6. Additional Results -- Ch. II. The Uniqueness Theorem. 7. The Transitivity Theorem. 8. The Fitting Subgroup of a Maximal Subgroup. 9. The Uniqueness Theorem -- Ch. III. Maximal Subgroups. 10. The Subgroups M[subscript [alpha]] and A[subscript [sigma]]. 11. Exceptional Maximal Subgroups. 12. The Subgroup E. 13. Prime Action -- Ch. IV. The Family of All Maximal Subgroups of G. 14. Maximal Subgroups of Type [actual symbol not reproducible] and Counting Arguments. 15. The Subgroup M[subscript F]. 16. The Main Results -- App. A: Prerequisites and p-Stability -- App. B: The Puig Subgroup -- App. C: The Final Contradiction -- App. D: CN-Groups of Odd Order -- App. E: Further Results of Feit and Thompson Feit-Thompson theorem Solvable groups p-Gruppe (DE-588)4174108-0 gnd Endliche Gruppe (DE-588)4014651-0 gnd |
| subject_GND | (DE-588)4174108-0 (DE-588)4014651-0 |
| title | Local analysis for the odd order theorem |
| title_auth | Local analysis for the odd order theorem |
| title_exact_search | Local analysis for the odd order theorem |
| title_full | Local analysis for the odd order theorem Helmut Bender and George Glauberman, with the assistance of Walter Carlip |
| title_fullStr | Local analysis for the odd order theorem Helmut Bender and George Glauberman, with the assistance of Walter Carlip |
| title_full_unstemmed | Local analysis for the odd order theorem Helmut Bender and George Glauberman, with the assistance of Walter Carlip |
| title_short | Local analysis for the odd order theorem |
| title_sort | local analysis for the odd order theorem |
| topic | Feit-Thompson theorem Solvable groups p-Gruppe (DE-588)4174108-0 gnd Endliche Gruppe (DE-588)4014651-0 gnd |
| topic_facet | Feit-Thompson theorem Solvable groups p-Gruppe Endliche Gruppe |
| url | https://doi.org/10.1017/CBO9780511665592 |
| work_keys_str_mv | AT benderhelmut localanalysisfortheoddordertheorem AT glaubermang localanalysisfortheoddordertheorem AT carlipwalter localanalysisfortheoddordertheorem |