Finite Groups II
17):~t? L It CIFDr- ! wei! unsre Weisheit Einfalt ist, From "Lohengrin", Richard Wagner At the time of the appearance of the first volume of this work in 1967, the tempestuous development of finite group theory had already made it virtually impossible to
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Editors
M. Artin S. S. Chern J. L. Doob A. Grothendieck E. Heinz F. Hirzebruch L. Hormander s. Mac Lane W. Magnus C. C. Moore J. K. Moser M. Nagata W. Schmidt D. s. Scott J. Tits B. L. van der Waerden Managing Editors B. Eckmann
s. R. s. Varadhan
B.Huppert N.Blackbum
Finite Groups II
Springer-Verlag Berlin Heidelberg New York 1982
Bertram Huppert Mathematisches Institut der Universitat SaarstraBe 21 D-6500 Mainz N orman Blackburn Department of Mathematics The University GB-Manchester M13 9 PL
Library of Congress Cataloging in Publication Data. Huppert, Bertram, 1927-. Finite groups II. (Grundlehren der mathematischen Wissenschaften; 242). Bibliography: p. Includes index. I. Finite groups. I. Blackburn, N. (Norman). II. Title. III. Series. QA 17l.B 577. 512'.22. 81-2287. ISBN-13: 978-3-642-67996-4 e-ISBN-13: 978-3-642-67994-0 DOl: 10.1007/978-3-642-67994-0 This work ist subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, reuse 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. © Springer-Verlag Berlin Heidelberg 1982
Softcover reprint of the hardcover 1st edition 1982
2141/3140-543210
In Memoriam
Reinhold Baer (1902-1979) Richard Brauer (1901-1977)
Preface
17):~t? L It CIFDrwei! unsre Weisheit Einfalt
!
ist,
From "Lohengrin", Richard Wagner
At the time of the appearance of the first volume of this work in 1967, the tempestuous development of finite group theory had already made it virtually impossible to give a complete presentation of the subject in one treatise. The present volume and its successor have therefore the more modest aim of giving descriptions of the recent development of certain important parts of the subject, and even in these parts no attempt at completeness has been made. Chapter VII deals with the representation theory of finite groups in arbitrary fields with particular attention to those of non-zero characteristic. That part of modular representation theory which is essentially the block theory of complex characters has not been included, as there are already monographs on this subject and others will shortly appear. Instead, we have restricted ourselves to such results as can be obtained by purely module-theoretical means. In Chapter VIII, the linear (and bilinear) methods which have proved useful in questions involving nilpotent groups are discussed. A major part of this is devoted to the classification of Suzuki 2-groups (see §7); while a complete classification is not obtained, the result proved is strong enough for an application to the determination of the Zassenhaus groups in Chapter XI. The standard procedure involves the use of Lie rings, and rather than attempting a theory of the connection between nilpotent groups and Lie rings, we give a number of applications
