The solution of the k(GV) problem /:
The <i>k(GV)</i> conjecture claims that the number of conjugacy classes (irreducible characters) of the semidirect product <i>GV</i> is bounded above by the order of <i>V</i>. Here <i>V</i> is a finite vector space and <i>G</i> a subgroup o...
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| Sprache: | English |
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London : Singapore ; Hackensack, NJ :
Imperial College Press ; Distributed by World Scientific Pub.,
©2007.
|
| Schriftenreihe: | Imperial College Press advanced texts in mathematics ;
v. 4. |
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| Online-Zugang: | Volltext |
| Zusammenfassung: | The <i>k(GV)</i> conjecture claims that the number of conjugacy classes (irreducible characters) of the semidirect product <i>GV</i> is bounded above by the order of <i>V</i>. Here <i>V</i> is a finite vector space and <i>G</i> a subgroup of <i>GL(V)</i> of order prime to that of <i>V</i>. It may be regarded as the special case of Brauer's celebrated <i>k(B)</i> problem dealing with <i>p</i>-blocks <i>B</i> of p-solvable groups (<i>p</i> a prime). Whereas Brauer's problem is still open in its generality, the <i>k(GV)</i> problem has recently been solved, completing the work of a series of aut. |
| Beschreibung: | 1 online resource (xiv, 232 pages). |
| Bibliographie: | Includes bibliographical references (pages 225-229) and index. |
| ISBN: | 9781860949715 1860949711 1281869465 9781281869463 9786611869465 6611869468 |
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| 245 | 1 | 4 | |a The solution of the k(GV) problem / |c Peter Schmid. |
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| 505 | 0 | |a 1. Conjugacy classes, characters, and Clifford Theory -- 2. Blocks of characters and Brauer's k(B) problem -- 3. The k(GV) problem -- 4. Symplectic and orthogonal modules -- 5. Real vectors -- 6. Reduced pairs of extraspecial type -- 7. Reduced pairs of quasisimple type -- 8. Modules without real vectors -- 9. Class numbers of permutation groups -- 10. The final stages of the proof -- 11. Possibilities for k(GV) = | |
| 520 | |a The <i>k(GV)</i> conjecture claims that the number of conjugacy classes (irreducible characters) of the semidirect product <i>GV</i> is bounded above by the order of <i>V</i>. Here <i>V</i> is a finite vector space and <i>G</i> a subgroup of <i>GL(V)</i> of order prime to that of <i>V</i>. It may be regarded as the special case of Brauer's celebrated <i>k(B)</i> problem dealing with <i>p</i>-blocks <i>B</i> of p-solvable groups (<i>p</i> a prime). Whereas Brauer's problem is still open in its generality, the <i>k(GV)</i> problem has recently been solved, completing the work of a series of aut. | ||
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| contents | 1. Conjugacy classes, characters, and Clifford Theory -- 2. Blocks of characters and Brauer's k(B) problem -- 3. The k(GV) problem -- 4. Symplectic and orthogonal modules -- 5. Real vectors -- 6. Reduced pairs of extraspecial type -- 7. Reduced pairs of quasisimple type -- 8. Modules without real vectors -- 9. Class numbers of permutation groups -- 10. The final stages of the proof -- 11. Possibilities for k(GV) = |
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| spelling | Schmid, Peter, 1941- https://id.oclc.org/worldcat/entity/E39PCjDk6vhQvj8DTVf7g8bKMK http://id.loc.gov/authorities/names/n2007068092 The solution of the k(GV) problem / Peter Schmid. London : Imperial College Press ; Singapore ; Hackensack, NJ : Distributed by World Scientific Pub., ©2007. 1 online resource (xiv, 232 pages). text txt rdacontent computer c rdamedia online resource cr rdacarrier ICP advanced texts in mathematics ; v. 4 Includes bibliographical references (pages 225-229) and index. Print version record. 1. Conjugacy classes, characters, and Clifford Theory -- 2. Blocks of characters and Brauer's k(B) problem -- 3. The k(GV) problem -- 4. Symplectic and orthogonal modules -- 5. Real vectors -- 6. Reduced pairs of extraspecial type -- 7. Reduced pairs of quasisimple type -- 8. Modules without real vectors -- 9. Class numbers of permutation groups -- 10. The final stages of the proof -- 11. Possibilities for k(GV) = The <i>k(GV)</i> conjecture claims that the number of conjugacy classes (irreducible characters) of the semidirect product <i>GV</i> is bounded above by the order of <i>V</i>. Here <i>V</i> is a finite vector space and <i>G</i> a subgroup of <i>GL(V)</i> of order prime to that of <i>V</i>. It may be regarded as the special case of Brauer's celebrated <i>k(B)</i> problem dealing with <i>p</i>-blocks <i>B</i> of p-solvable groups (<i>p</i> a prime). Whereas Brauer's problem is still open in its generality, the <i>k(GV)</i> problem has recently been solved, completing the work of a series of aut. English. Kernel functions. http://id.loc.gov/authorities/subjects/sh85072061 Noyaux (Mathématiques) MATHEMATICS Functional Analysis. bisacsh Kernel functions fast Imperial College of Science, Technology and Medicine. http://id.loc.gov/authorities/names/n89624734 Print version: Schmid, Peter, 1941- Solution of the k(GV) problem. London : Imperial College Press ; Singapore ; Hackensack, NJ : Distributed by World Scientific Pub., ©2007 (DLC) 2007039136 Imperial College Press advanced texts in mathematics ; v. 4. http://id.loc.gov/authorities/names/no2007087803 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=236042 Volltext |
| spellingShingle | Schmid, Peter, 1941- The solution of the k(GV) problem / Imperial College Press advanced texts in mathematics ; 1. Conjugacy classes, characters, and Clifford Theory -- 2. Blocks of characters and Brauer's k(B) problem -- 3. The k(GV) problem -- 4. Symplectic and orthogonal modules -- 5. Real vectors -- 6. Reduced pairs of extraspecial type -- 7. Reduced pairs of quasisimple type -- 8. Modules without real vectors -- 9. Class numbers of permutation groups -- 10. The final stages of the proof -- 11. Possibilities for k(GV) = Kernel functions. http://id.loc.gov/authorities/subjects/sh85072061 Noyaux (Mathématiques) MATHEMATICS Functional Analysis. bisacsh Kernel functions fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85072061 |
| title | The solution of the k(GV) problem / |
| title_auth | The solution of the k(GV) problem / |
| title_exact_search | The solution of the k(GV) problem / |
| title_full | The solution of the k(GV) problem / Peter Schmid. |
| title_fullStr | The solution of the k(GV) problem / Peter Schmid. |
| title_full_unstemmed | The solution of the k(GV) problem / Peter Schmid. |
| title_short | The solution of the k(GV) problem / |
| title_sort | solution of the k gv problem |
| topic | Kernel functions. http://id.loc.gov/authorities/subjects/sh85072061 Noyaux (Mathématiques) MATHEMATICS Functional Analysis. bisacsh Kernel functions fast |
| topic_facet | Kernel functions. Noyaux (Mathématiques) MATHEMATICS Functional Analysis. Kernel functions |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=236042 |
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