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Permutation groups are one of the oldest topics in algebra. Their study has recently been revolutionized by new developments, particularly the Classification of Finite Simple Groups, but also relations with logic and combinatorics, and importantly, computer algebra systems have been introduced that can deal with large permutation groups. This text summarizes these developments, including an introduction to relevant computer algebra systems, sketch proofs of major theorems, and many examples of applying the Classification of Finite Simple Groups. It is aimed at beginning graduate students and experts in other areas, and grew from a short course at the EIDMA institute in Eindhoven.
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LONDON MATHEMATICAL SOCIETY STUDENT TEXTS
Managing editor: Professor C.M. Series, Mathematics Institute University of Warwick, Coventry CV4 7AL, United Kingdom
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London Mathematical Society Student Texts 45
Permutation Groups
Peter J. Cameron Queen Mary and Westfield College, London
AMBRIDGE
UNIVERSITY PRESS
CAMBRIDGE UNIVERSITY PRESS Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, SAo Paulo
Cambridge University Press The Edinburgh Building, Cambridge CB2 2RU, UK Published in the United States of America by Cambridge University Press, New York www.cambridge.org Information on this title: www.cambridge.org/9780521653022
© Peter J. Cameron 1999
This publication is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published 1999
A catalogue record for this publication is available from the British Library ISBN-13 978-0-521-65302-2 hardback ISBN-10 0-521-65302-9 hardback ISBN-13 978-0-521-65378-7 paperback ISBN-10 0-