Symplectic Amalgams
The aim of this book is the classification of symplectic amalgams - structures which are intimately related to the finite simple groups. In all there sixteen infinite families of symplectic amalgams together with 62 more exotic examples. The classificatio
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Springer-Verlag London Ltd.
Christopher Parker
Peter Rowley
Symplectic Amalgams
,
Springer
Christopher Parker School of Mathematics and Statistics University of Birmingham Edgbaston Birmingham BIS 2TT
UK
Peter Rowley Department of Mathematics University of Manchester Institute of Science and Technology PO Box 88 Manchester M60IQD
UK
British Library Cataloguing in Publication Data Parker, Christopher Symplectic amalgams. - (Springer monographa in mathematics) I.Symplectic groups 2.Amalgams (Group theory) I.Title II.Rowley, Peter 512.2 ISBN 978-1-4471- 1088-0 ISBN 978-1-4471-0165-9 (eBook) DOI 10.1007/978-1-4471-0165-9
Library of Congress Cataloging-in-Publication Data
A catalog record for this book is available from the Library of Congress. Mathematics Subject Classification (1991): 20006, 20006 Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms of licences issued by the Copyright Licensing Agency. Enquiries concerning reproduction outside those terms should be sent to the publishers. Springer Monographs in Mathematics ISSN 1439-7382 ISBN 978-1-4471-1088-0
http://www.springer.co.uk @ Springer-Verlag London 2002 Originally published by Springer-Verlag London Limited in 2002 Softcover reprint of the hardcover 1st edition 2002 The use of registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant laws and regulations and therefore free for general use.
The publisher makes no representation, express or implied, with regard to the accuracy of the information contained in this book and cannot accept any legal responsibility or liability for any errors or omissions that may be made. Typesetting: Camera-ready by the authors 12/3830-543210 Printed on acid-free paper SPIN 10791807
To the memory of our fathers John Victor Parker 1931-1996
Sydney John Rowley 1922-1998
Preface
In the past 50 years group theory has experienced phenomenal growth. To a great extent this was ignited and sustained by attempts to understand and, ultimately, classify the finite simple groups. The pioneering work of Brauer [19, 20, 21]' and later Suzuki [175, 176], on centralizers of involutions and the systematization of groups of Lie type begun by Chevalley [33] were, in a sense, the calm before the storm. Perhaps more than any other result, the Odd Order Theorem [52] by Feit and Thompson which states that a group of odd order is soluble was the trigger for the subsequent intense research activity on finite simple groups. An enormous number of mathematicians joined the fray in the 1960's and 1970's and their work led to the extraordinary achievement of the classification of the finite simple groups. Th
