The Solution of the K(Gv) Problem.

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The k(GV) conjecture claims that the number of conjugacy classes (irreducible characters) of the semidirect product GV is bounded above by the order of V . Here V is a finite vector space and G a subgroup of GL(V) of order prime to that of V . It may be regarded as the special case of Brauer's...

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Détails bibliographiques
Cote:Libro Electrónico
Auteur principal: Schmid, Peter
Format: Électronique eBook
Langue:Inglés
Publié: Singapore : World Scientific Publishing Company, 2007.
Collection:Imperial College Press advanced texts in mathematics.
Sujets:
Kernel functions.
Noyaux (Mathématiques)
Kernel functions
Accès en ligne:Texto completo

MARC

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020 |a 9781860949715 
020 |a 1860949711 
020 |z 9781860949708  |q (hardcover ;  |q alk. paper) 
020 |z 1860949703  |q (hardcover ;  |q alk. paper) 
029 1 |a AU@  |b 000055973900 
029 1 |a DEBBG  |b BV044178789 
029 1 |a DEBSZ  |b 405244460 
035 |a (OCoLC)879023533 
050 4 |a QA353.K47  |b S36 2007 
082 0 4 |a 515.7223 
049 |a UAMI 
100 1 |a Schmid, Peter. 
245 1 4 |a The Solution of the K(Gv) Problem. 
260 |a Singapore :  |b World Scientific Publishing Company,  |c 2007. 
300 |a 1 online resource (248 pages) 
336 |a text  |b txt  |2 rdacontent 
337 |a computer  |b c  |2 rdamedia 
338 |a online resource  |b cr  |2 rdacarrier 
490 1 |a Icp Advanced Texts in Mathematics 
588 0 |a Print version record. 
520 |a The k(GV) conjecture claims that the number of conjugacy classes (irreducible characters) of the semidirect product GV is bounded above by the order of V . Here V is a finite vector space and G a subgroup of GL(V) of order prime to that of V . It may be regarded as the special case of Brauer's celebrated k(B) problem dealing with p -blocks B of p-solvable groups (p a prime). Whereas Brauer's problem is still open in its generality, the k(GV) problem has recently been solved, completing the work of a series of authors over a period of more than forty years. In this book the developments, ideas. 
504 |a Includes bibliographical references (pages 225-229) and index. 
505 0 |a Preface; 1. Conjugacy Classes, Characters, and Clifford Theory; 1.1 Class Functions and Characters; 1.2 Induced and Tensor-induced Modules; 1.3 Schur's Lemma; 1.4 Brauer's Permutation Lemma; 1.5 Algebraic Conjugacy; 1.6 Coprime Actions; 1.7 Invariant and Good Conjugacy Classes; 1.8 Nonstable Clifford Theory; 1.9 Stable Clifford Theory; 1.10 Good Conjugacy Classes and Extendible Characters; 2. Blocks of Characters and Brauer's k(B) Problem; 2.1 Modular Decomposition and Brauer Characters; 2.2 Cartan Invariants and Blocks; 2.3 Defect and Defect Groups; 2.4 The Brauer-Feit Theorem. 
505 8 |a 2.5 Higher Decomposition Numbers, Subsections2.6 Blocks of p-Solvable Groups; 2.7 Coprime FpX-Modules; 3. The k(GV) Problem; 3.1 Preliminaries; 3.2 Transitive Linear Groups; 3.3 Subsections and Point Stabilizers; 3.4 Abelian Point Stabilizers; 4. Symplectic and Orthogonal Modules; 4.1 Self-dual Modules; 4.2 Extraspecial Groups; 4.3 Holomorphs; 4.4 Good Conjugacy Classes Once Again; 4.5 Some Weil Characters; 4.6 Symplectic and Orthogonal Modules; 5. Real Vectors; 5.1 Regular, Abelian and Real Vectors; 5.2 The Robinson{Thompson Theorem; 5.3 Search for Real Vectors; 5.4 Clifford Reduction. 
505 8 |a 5.5 Reduced Pairs5.6 Counting Methods; 5.7 Two Examples; 6. Reduced Pairs of Extraspecial Type; 6.1 Nonreal Reduced Pairs; 6.2 Fixed Point Ratios; 6.3 Point Stabilizers of Exponent 2; 6.4 Characteristic 2; 6.5 Extraspecial 3-Groups; 6.6 Extraspecial 2-Groups of Small Order; 6.7 The Remaining Cases; 7. Reduced Pairs of Quasisimple Type; 7.1 Nonreal Reduced Pairs; 7.2 Regular Orbits; 7.3 Covering Numbers, Projective Marks; 7.4 Sporadic Groups; 7.5 Alternating Groups; 7.6 Linear Groups; 7.7 Symplectic Groups; 7.8 Unitary Groups; 7.9 Orthogonal Groups; 7.10 Exceptional Groups. 
505 8 |a 8. Modules without Real Vectors8.1 Some Fixed Point Ratios; 8.2 Tensor Induction of Reduced Pairs; 8.3 Tensor Products of Reduced Pairs; 8.4 The Riese-Schmid Theorem; 8.5 Nonreal Induced Pairs, Wreath Products; 9. Class Numbers of Permutation Groups; 9.1. The Partition Function; 9.2 Preparatory Results; 9.3 The Liebeck-Pyber Theorem; 9.4 Improvements; 10. The Final Stages of the Proof; 10.1 Class Numbers for Nonreal Reduced Pairs; 10.2 Counting Invariant Conjugacy Classes; 10.3 Nonreal Induced Pairs; 10.4 Characteristic 5; 10.5 Summary; 11. Possibilities for k(GV) = jV j; 11.1 Preliminaries. 
505 8 |a 11.2 Some Congruences11.3 Reduced Pairs; 12. Some Consequences for Block Theory; 12.1 Brauer Correspondence; 12.2 Clifford Theory of Blocks; 12.3 Blocks with Normal Defect Groups; 13. The Non-Coprime Situation; Appendix A: Cohomology of Finite Groups; Appendix B: Some Parabolic Subgroups; Appendix C: Weil Characters; Bibliography; List of Symbols; Index. 
590 |a ProQuest Ebook Central  |b Ebook Central Academic Complete 
650 0 |a Kernel functions. 
650 6 |a Noyaux (Mathématiques) 
650 7 |a Kernel functions  |2 fast 
776 0 8 |i Print version:  |z 9781860949708 
830 0 |a Imperial College Press advanced texts in mathematics. 
856 4 0 |u https://ebookcentral.uam.elogim.com/lib/uam-ebooks/detail.action?docID=1679367  |z Texto completo 
938 |a EBL - Ebook Library  |b EBLB  |n EBL1679367 
994 |a 92  |b IZTAP 

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