Topics in Cohomology of Groups
The book is a mostly translated reprint of a report on cohomology of groups from the 1950s and 1960s, originally written as background for the Artin-Tate notes on class field theory, following the cohomological approach. This report was first published (i
- PDF / 8,407,463 Bytes
- 231 Pages / 432 x 666 pts Page_size
- 87 Downloads / 202 Views
1625
Springer Berlin Heidelberg New York Barcelona Budapest Hong Kong London Milan Paris Santa Clara Singapore Tokyo
Serge Lang
Topics in Cohomology of Groups
Springer
Author Serge Lang Mathematics Derpartment Yale University, Box 208 283 10 Hillhouse Avenue New Haven, CT 06520-8283, USA
Library of Congress Cataloging-in-Publication Data
Lang. Serge. 1927[Rapport sur la cohomologle des groupes. Engllsh] Topics in cohomology of groups / Serge Lang. p. cm. -- (Lecture notes in mathematics 1625) Includes bt b l iographical references t p , ) and tnc ax . ISBN 3-540-61181-9 (alk. paper) 1. Class field theory. 2. Group theory. 3. Homology theory. I. Title. II. Serles: Lecture notes ln mathematics (Springer -Verlag) ; 1625. QA247.L3513 1996 512' .74--dc20 96-26607
The first part of this book was originally published in French with the title "Rapport sur la cohomologie des groupes" by Benjamin Inc., New York, 1996. It was translated into English by the author for this edition. The last part (pp. 188-215) is new to this edition.
Mathematics Subject Classification (1991): IIS25, llS31, 20106, 12G05, 12010 ISBN 3-540-61181-9 Springer-Verlag Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part ofthe material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution under the German Copyright Law. © Springer-Verlag Berlin Heidelberg 1996 Printed in Germany Typesetting: Camera-ready TEX output by the author SPIN: 10479722 46/3142-543210 - Printed on acid-free paper
Contents Chapter I. Existence and Uniqueness
§1. The abstract uniqueness theorem Notations, and the uniqueness theorem in Mod( G) Existence of the cohomological functor on Mod( G) Explicit computations Cyclic groups
§2. §3. §4. §5.
3 9 20 29 32
Chapter II. Relations with Subgroups
§1. §2. §3. §4.
Various morphisms Sylow subgroups Induced representations Double cosets
37 50 52 58
Chapter III. Cohomological Triviality
§1. The twins theorem §2. The triplets theorem §3. Splitting module and Tate's theorem
62 68 70
Chapter IV. Cup Products
§1. §2. §3. §4. §5. §6. §7. §8.
Erasability and uniqueness Existence Relations with subgroups The triplets theorem The cohomology ring and duality Periodicity The theorem of Tate-Nakayama Explicit Nakayama maps
73 83 87 88 89 95 98 101
VI
Chapter V. Augmented Products §1. Definitions §2. Existence §3. Some properties
109 112 113
Chapter VI. Spectral Sequences §1. Definitions §2. The Hochschild-Serre spectral sequence §3. Spectral sequences and cup products Chapter VII. §1. §2. §3. §4. §5. §6.
116 118 121
Groups of Galois Type (U npublished article
Data Loading...
