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372 Proceed ings of the Second International Conference on

The Theory of Groups Australian National University, August 13-24, 1973

Edited by M. F. Newman

Springer-Verlag Berlin Heidelberg GmbH 1974

M. F. Newman Dept. of Mathematics Australian National University Institute of Advanced Studies Canberra, ACT 2600/ Australia

Library of Congrcss Cataloging in Publication Dat.

International Conference on the Theory of Groups, 2d, Australian National University, 1973. Proceedings. (Lecture notes in mathematics (Berlin) , 372) Groups, Theory of--Congresses. L Newman, Michael Frederick, 193 1;ed. II. Series. Q,A3.L28 no. 372 [Q,Al71] 512' .22 74-13872 l.

AMS Subject Classifications (1970): 20xx, 22xx

ISBN 978-3-540-06845-7 ISBN 978-3-662-21571-5 (eBook) DOI 10.1007/978-3-662-21571-5 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re·use of illustrations, broadcasting, reproductien by photocopying machine or similar means, and storage in data banks. Under § 54 of the German Copyright Law where copies are made for ether than private use, a fee is payable to the publisher, the amount of the fee to be determined by agreement with the publisher. @

by Springer-Verlag Berlin Heidelberg 1974

Ursprünglich erschienen bei Springer·Veriag Berlin . Heidelberg . New York Offsetdruck: Julius Beltz, Hemsbach/Bergstr.

PREFACE

This volume consists of papers presented to the Second International Conference on the Theory of Groups held in Canberra in August 1973 together with areport by the chairman of the Organizing Committee and a collection of problems. The manuscripts were typed by Mrs Geary, the bulk of the bibliographie work was done by Mrs Pinkerton, and a number of colleagues helped with proof-reading; Professor Neumann, Drs Cossey, Kovacs, MeDougall, Praeger, Pride, Rangaswamy and Stewart.

I here reeord my thanks to all these people for their lightening of the

editorial burden.

M.F. Newrnan

CONTENTS

Introduction .. ~yan,

1

8

Periodic groups of odd exponent

Reinhold Baer, Einbettungseigenschaften von Normalteilern:

der Schluss vom

Endlichen aufs Unendliche

13

D.W. Barnes, Characterisation of the groups with the Gaschütz cohomology property

63

Gi Ibert Baumslag, Finitely presented metabe1ian groups

65

Gi Ibert Baumslag, Some problems on one-relator groups

75

A.J.

Ba~,

J. Kautsky and J.W. Wamsley, Computation in nilpotent groups

(application)

82

Wi I I iam W. Boone, Between logic and group theory

90

Richard Brauer, On the structure of blocks of characters of finite groups

103

A.M. Brunner, Transitivity-systems of certain one-relator groups

131

Egg8r M. Bryant, Characteristic subgroups of free groups ~y~,

Metabe1ian varieties of groups

141 150

R.A. Bryce and John Cossey, Subdirect product c10sed Fitting c1asses

158

R.G. Burns, On the rank of the intersection of subgroups of a Fuchsian group

165

Kim Ki-Hang Butler, Subgroups of binary relations

188

M.C.R. Butler, The

197