A Remark on Integral Duality
The integral duality theorem [3; p. 250] provides isomorphisms for all k ≥ 0, \( \left( {{H^k}\left( {G,B} \right)} \right)* \cong {H_k}\left( {G,B*} \right) \) where G is a finite group, B is a G-module, and ( )* = HomZ( ,Q/Z). This is usually proved usi
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Abelian Group Theory Proceedings of the Conference held at the University of Hawaii, Honolulu, USA December 28, 1982 - January 4,1983
Edited by R. Gobel. L. Lady and A. Mader
Springer-Verlag Berlin Heidelberg GmbH 1983
Editors
Rudiger Gobel FB 6 - Mathematik, Universitat Essen, Gesamthochschule Universitatsstr. 3, 4300 Essen 1, Federal Republic of Germany Lee Lady Adolf Mader Department of Mathematics, University of Hawaii 2565 The Mall, Honolulu, Hawai 96822, USA
AMS Subject Classifications (1982): 3Cxx, 3Exx, 3Fxx, 12Axx, 12Bxx, 12Fxx, 13Axx,13Cxx, 13Dxx, 13 Exx, 13Fxx, 13Gxx, 13Hxx, 13Jxx, 16A46, 18Exx, 18 Fxx, 18Gxx, 20-04, 20 Kxx, 22Bxx ISBN 978-3-540-12335-4 ISBN 978-3-662-21560-9 (eBook) DOI 10.1007/978-3-662-21560-9 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under § 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to "Verwertungsgesellschaft Wort", Munich.
© by Springer-Verlag Berlin Heidelberg 1983 Originally published by Springer-Verlag Berlin Heidelberg New York in 1983 2146/3140-543210
PREFACE
A conference on Abelian Group Theory was held at the Manoa Campus of the University of Hawaii from December 28, 1982 to January 4, 1983.
It was probably the best attended conference on Abelian
Group Theory to date with 55 participants from allover the world and the busiest one with 49 talks.
A special feature were general
interest lectures by Hyman Bass, Columbia University, on "Non-linear Algebra", and by Claus Michael Ringel, Uni versiUit Bielefeld, on "Representations of Algebras".
The Conference offered surveys by
Laszlo Fuchs, Tulane University, on "Torsion Modules over Valuation Rings", Fred Richman, New Mexico State University, on "Mixed Groups", Paul Eklof, University of California at Irvine, on "Set Theory and Structure Theorems", Rudiger Gobel, Un:i:versitat Essen on "Endomorphism Rings", and Lee Lady, University of Hawaii, on "Torsion Free Groups of Finite Rank".
The research reports attested to lively activity in the
traditional and in new areas of inquiry within and around Abelian Group Theory.
The best represented groups were those of finite rank without
torsion, a field employing increasingly sophisticated tools from ring theory and algebraic number theory.
The use of set theoretic methods
continues to flourish after the pioneering work of Saharon Shelah in the 1970s, and is delivering impressive results. This volume contains the papers of the participants df the Conferencean6 a number of additional articles of others who could not or did not corne.
It reflects faithfully and almost completely the present;
status of Abelian Group Theory and should be invaluable to those in Abelian Groups and those who want to be informed. Rudiger GObel, Universitat Essen Lee Lady and Adolf Mader, Unive
