Around Burnside
Perhaps it is not inappropriate for me to begin with the comment that this book has been an interesting challenge to the translator. It is most unusual, in a text of this type, in that the style is racy, with many literary allusions and witticisms: not th
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Editorial Board E. Bombieri, Princeton S. Feferman, Stanford M. Gromov, Bures-sur-Yvette N. H. Kuiper, Bures-sur-Yvette H. W. Lenstra, Jr., Berkeley R. Remmert (Managing Editor), Munster W. Schmid, Cambridge, Mass. J -Po Serre, Paris J. Tits, Paris K. K. Uhlenbeck, Austin
A. 1. Kostrikin Professor, V. A. Steklov Institute Vavilov Street 42 II 7966, GSP-I, Moscow USSR Dr. James Wiegold Professor, School of Mathematics University of Wales College of Cardiff Senghenydd Road Cardiff CF2 4AG, Wales, U.K.
Original Russian language edition, entitled "BOKPYf 6EPHCAIIJAA", published by MOCKBA «HAYKA». All rights reserved.
Mathematics Subject Classification (1980): 1IF41, llG18, 11120 ISBN-13 :978-3-642-74326-9 e-ISBN-13: 978-3-642-74324-5 DOl: 10.1007/978-3-642-74324-5 Library of Congress Cataloging-in-Publication Data Kostrikin, A. I. (Aleksef Ivanovich) [Vokrug Bernsaida. English] Around Burnside I A. 1. Kostrikin. p. cm. (Ergebnisse der Mathematik und ihrer Grenzgebiete : 3. Folge. Bd. 20) Translation of: Vokrug Bernsafda. ISBN -13: 978-3-642-74326·9 1. Burnside problem. I. Title. II. Series. QAI71.K67413 1990 512·.2--dc20 89-26244 This work is subject to copyright. All rights are reserved. whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations. recitation. broadcasting. reproduction on microfilms or in other ways, and storage in data banks. Duplication of this publication or parts thereof is only permitted under the provisions of the German Copyright Law of September 9. 1965, in its current version, and a copyright fee must always be paid. Violations fall under the prosecution act of the German Copyright Law.
© Springer-Verlag Berlin Heidelberg 1990 Softcover reprint of the hardcover 1st edition 1990 Typesetting: Macmillan India Ltd .. India. 2141/3020-543210 - Printed on acid-free paper
In Memory of my Parents Kostrikin, Ivan Vukolovich (1887-1968) Kostrikin, Evdokiya Stepanovna (1887-1971)
Translator's Preface
Perhaps it is not inappropriate for me to begin with the comment that this book has been an interesting challenge to the translator. It is most unusual, in a text of this type, in that the style is racy, with many literary allusions and witticisms: not the easiest to translate, but a source of inspiration to continue through material that could daunt by its combinatorial complexity. Moreover, there have been many changes to the text during the translating period, reflecting the ferment that the subject of the restricted Burnside problem is passing through at present. I concur with Professor Kostrikin's "Note in Proof', where he describes the book as fortunate. I would put it slightly differently: its appearance has surely been partly instrumental in inspiring much endeavour, including such things as the paper of A. I. Adian and A. A. Razborov producing the first published recursive upper bound for the order of the universal finite group B(d,p) of prime exponent (the English version contains a different treatment of this result
