Representations of Solvable Groups

Erscheinungsjahr 2004
ISBN: 978-0-521-39739-1
Verlag: Cambridge University Press

Buch, Englisch, Band 185, 314 Seiten, Format (B × H): 152 mm x 229 mm, Gewicht: 515 g

Reihe: London Mathematical Society Lecture Note Series

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.

Autoren/Hrsg.

Manz, Olaf

Wolf, Thomas R.

Cassels, J. W. S.

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie

Inhaltsverzeichnis

Preliminaries; 1. Solvable subgroups of linear groups; 2. Solvable permutation groups; 3. Module actions with large centralizers; 4. Prime power divisors of character degrees; 5. Complexity of character degrees; 6. p-special characters.