Structure Theory for Canonical Classes of Finite Groups
This book offers a systematic introduction to recent achievements and development in research on the structure of finite non-simple groups, the theory of classes of groups and their applications. In particular, the related systematic theories are consider
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Wenbin Guo
Structure Theory for Canonical Classes of Finite Groups
2123
Wenbin Guo School of Mathematical Sciences University of Science and Technology of China Hefei China
ISBN 978-3-662-45746-7 DOI 10.1007/978-3-662-45747-4
ISBN 978-3-662-45747-4 (eBook)
Library of Congress Control Number: 2014958309 Mathematics subject Classification: 20D10, 20D15, 20D20, 20D25, 20D30, 20D35, 20D40, 20E28 Springer Heidelberg New York Dordrecht London © Springer-Verlag Berlin Heidelberg 2015 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Preface
The central challenge of any mathematical theory is to provide reasonable classifications and constructive descriptions of the investigating objects that are most useful in diverse applications. At the same time, we realize that the purpose is to support new methods of investigation, which, in the end, constitute ideological riches of the given theory. For example, the development of the theory of finite non-simple groups in the past 50 years has clearly shown this tendency. Although the theory of finite groups has never been lacking in general methods, ideas, or unsolved problems, the large body of results has inevitably brought us to the point of needing to develop new methods to systemize the material. One example of such systemizing is the idea of Gaschüts that the use of some given classes of groups, called saturated formations, is convenient for investigating the inner structure of finite groups. The theory of formation initially found wide application in the research of finite groups and infinite groups, as reflected in a series of classical monographs. The first is the famous book of Huppert [248]. The book, which described research in the structure of finite groups, attracted the attention of many specialists in algebra. The investigation involving saturated and partially saturated (ω-saturated or soluble ω-saturated) formations be
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