Representations of solvable groups /:
Representation theory plays an important role in algebra, and in this book Manz and Wolf concentrate on that part of the theory which relates to solvable groups. The authors begin by studying modules over finite fields, which arise naturally as chief factors of solvable groups. The information obtai...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge ; New York :
Cambridge University Press,
©1993.
|
| Schriftenreihe: | London Mathematical Society lecture note series ;
185. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | Representation theory plays an important role in algebra, and in this book Manz and Wolf concentrate on that part of the theory which relates to solvable groups. The authors begin by studying modules over finite fields, which arise naturally as chief factors of solvable groups. The information obtained can then be applied to infinite modules, and in particular to character theory (ordinary and Brauer) of solvable groups. The authors include proofs of Brauer's height zero conjecture and the Alperin-McKay conjecture for solvable groups. Gluck's permutation lemma and Huppert's classification of solvable two-transive permutation groups, which are essentially results about finite modules of finite groups, play important roles in the applications and a new proof is given of the latter. Researchers into group theory, representation theory, or both, will find that this book has much to offer. |
| Beschreibung: | 1 online resource (xi, 302 pages) |
| Bibliographie: | Includes bibliographical references (pages 293-298) and index. |
| ISBN: | 9781107361652 1107361656 9780511525971 0511525974 |
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| 520 | |a Representation theory plays an important role in algebra, and in this book Manz and Wolf concentrate on that part of the theory which relates to solvable groups. The authors begin by studying modules over finite fields, which arise naturally as chief factors of solvable groups. The information obtained can then be applied to infinite modules, and in particular to character theory (ordinary and Brauer) of solvable groups. The authors include proofs of Brauer's height zero conjecture and the Alperin-McKay conjecture for solvable groups. Gluck's permutation lemma and Huppert's classification of solvable two-transive permutation groups, which are essentially results about finite modules of finite groups, play important roles in the applications and a new proof is given of the latter. Researchers into group theory, representation theory, or both, will find that this book has much to offer. | ||
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| contents | Cover; Half-title; Title; Copyright; Contents; Preface; Acknowledgments; Chap. 0 Preliminaries; Chap. I Solvable subgroups of linear groups; 1 Quasi-primitive linear groups; 2 Semi-linear and small linear groups; 3 Bounds for the order and the derived length of linear groups; Chap. II Solvable permutation groups; 4 Orbit sizes of p-groups and the existence of regular orbits; 5 Solvable permutation groups and the existence of regular orbits on the power set; 6 Solvable doubly transitive permutation groups; 7 Regular orbits of Sylow subgroups of solvable linear groups |
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| spelling | Manz, Olaf. Representations of solvable groups / Olaf Manz and Thomas R. Wolf. Cambridge ; New York : Cambridge University Press, ©1993. 1 online resource (xi, 302 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier London Mathematical Society lecture note series ; 185 Includes bibliographical references (pages 293-298) and index. Print version record. Representation theory plays an important role in algebra, and in this book Manz and Wolf concentrate on that part of the theory which relates to solvable groups. The authors begin by studying modules over finite fields, which arise naturally as chief factors of solvable groups. The information obtained can then be applied to infinite modules, and in particular to character theory (ordinary and Brauer) of solvable groups. The authors include proofs of Brauer's height zero conjecture and the Alperin-McKay conjecture for solvable groups. Gluck's permutation lemma and Huppert's classification of solvable two-transive permutation groups, which are essentially results about finite modules of finite groups, play important roles in the applications and a new proof is given of the latter. Researchers into group theory, representation theory, or both, will find that this book has much to offer. Cover; Half-title; Title; Copyright; Contents; Preface; Acknowledgments; Chap. 0 Preliminaries; Chap. I Solvable subgroups of linear groups; 1 Quasi-primitive linear groups; 2 Semi-linear and small linear groups; 3 Bounds for the order and the derived length of linear groups; Chap. II Solvable permutation groups; 4 Orbit sizes of p-groups and the existence of regular orbits; 5 Solvable permutation groups and the existence of regular orbits on the power set; 6 Solvable doubly transitive permutation groups; 7 Regular orbits of Sylow subgroups of solvable linear groups Solvable groups. http://id.loc.gov/authorities/subjects/sh85124740 Representations of groups. http://id.loc.gov/authorities/subjects/sh85112944 Permutation groups. http://id.loc.gov/authorities/subjects/sh85099993 Groupes résolubles. Représentations de groupes. Groupes de permutations. MATHEMATICS Group Theory. bisacsh Permutation groups fast Representations of groups fast Solvable groups fast Auflösbare Gruppe gnd http://d-nb.info/gnd/4245706-3 Darstellung Mathematik gnd http://d-nb.info/gnd/4128289-9 Endliche auflösbare Gruppe gnd http://d-nb.info/gnd/4291485-1 Darstellungstheorie gnd http://d-nb.info/gnd/4148816-7 Groepen (wiskunde) gtt Représentations de groupes. ram Groupes de permutation. ram Wolf, Thomas R. Print version: Manz, Olaf. Representations of solvable groups. Cambridge ; New York : Cambridge University Press, ©1993 0521397391 (DLC) 94112292 (OCoLC)28981606 London Mathematical Society lecture note series ; 185. http://id.loc.gov/authorities/names/n42015587 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=552410 Volltext |
| spellingShingle | Manz, Olaf Representations of solvable groups / London Mathematical Society lecture note series ; Cover; Half-title; Title; Copyright; Contents; Preface; Acknowledgments; Chap. 0 Preliminaries; Chap. I Solvable subgroups of linear groups; 1 Quasi-primitive linear groups; 2 Semi-linear and small linear groups; 3 Bounds for the order and the derived length of linear groups; Chap. II Solvable permutation groups; 4 Orbit sizes of p-groups and the existence of regular orbits; 5 Solvable permutation groups and the existence of regular orbits on the power set; 6 Solvable doubly transitive permutation groups; 7 Regular orbits of Sylow subgroups of solvable linear groups Solvable groups. http://id.loc.gov/authorities/subjects/sh85124740 Representations of groups. http://id.loc.gov/authorities/subjects/sh85112944 Permutation groups. http://id.loc.gov/authorities/subjects/sh85099993 Groupes résolubles. Représentations de groupes. Groupes de permutations. MATHEMATICS Group Theory. bisacsh Permutation groups fast Representations of groups fast Solvable groups fast Auflösbare Gruppe gnd http://d-nb.info/gnd/4245706-3 Darstellung Mathematik gnd http://d-nb.info/gnd/4128289-9 Endliche auflösbare Gruppe gnd http://d-nb.info/gnd/4291485-1 Darstellungstheorie gnd http://d-nb.info/gnd/4148816-7 Groepen (wiskunde) gtt Représentations de groupes. ram Groupes de permutation. ram |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85124740 http://id.loc.gov/authorities/subjects/sh85112944 http://id.loc.gov/authorities/subjects/sh85099993 http://d-nb.info/gnd/4245706-3 http://d-nb.info/gnd/4128289-9 http://d-nb.info/gnd/4291485-1 http://d-nb.info/gnd/4148816-7 |
| title | Representations of solvable groups / |
| title_auth | Representations of solvable groups / |
| title_exact_search | Representations of solvable groups / |
| title_full | Representations of solvable groups / Olaf Manz and Thomas R. Wolf. |
| title_fullStr | Representations of solvable groups / Olaf Manz and Thomas R. Wolf. |
| title_full_unstemmed | Representations of solvable groups / Olaf Manz and Thomas R. Wolf. |
| title_short | Representations of solvable groups / |
| title_sort | representations of solvable groups |
| topic | Solvable groups. http://id.loc.gov/authorities/subjects/sh85124740 Representations of groups. http://id.loc.gov/authorities/subjects/sh85112944 Permutation groups. http://id.loc.gov/authorities/subjects/sh85099993 Groupes résolubles. Représentations de groupes. Groupes de permutations. MATHEMATICS Group Theory. bisacsh Permutation groups fast Representations of groups fast Solvable groups fast Auflösbare Gruppe gnd http://d-nb.info/gnd/4245706-3 Darstellung Mathematik gnd http://d-nb.info/gnd/4128289-9 Endliche auflösbare Gruppe gnd http://d-nb.info/gnd/4291485-1 Darstellungstheorie gnd http://d-nb.info/gnd/4148816-7 Groepen (wiskunde) gtt Représentations de groupes. ram Groupes de permutation. ram |
| topic_facet | Solvable groups. Representations of groups. Permutation groups. Groupes résolubles. Représentations de groupes. Groupes de permutations. MATHEMATICS Group Theory. Permutation groups Representations of groups Solvable groups Auflösbare Gruppe Darstellung Mathematik Endliche auflösbare Gruppe Darstellungstheorie Groepen (wiskunde) Groupes de permutation. |
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| work_keys_str_mv | AT manzolaf representationsofsolvablegroups AT wolfthomasr representationsofsolvablegroups |