Proceedings of the Second International Conference on The Theory of Groups
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372 Proceedings of the Second International Conference on
The Theory of Groups Australian National University, August 13-24, 1973
Edited by M. F. Newman IIIIII I I
Springer-Verlag Berlin. Heidelberg- New York 1974
M. F. Newman Dept. of Mathematics Australian National University Institute of Advanced Studies Canberra, ACT 2600/Australia
Library of Congress Cataloging in Publication Data
International Conference on the Theory of Groups, 2d, A~astrali~n National University, 1973. Proceedings. (Lecture no%es in mathematics (Berlin), 372) i. Groups, Theory of--Congresses. I. Newman, Michael Frederick, 1934ed. II. Series. ~3.L28 no. 372 [QAI71] 512'.22 74-13872
AMS Subject Classifications (1970): 20xx, 22 xx ISBN 3-540-06845-7 Springer-Verlag Berlin • Heidelberg - New York ISBN 0-387-06845-7 Springer-Verlag New Y o r k . Heidelberg • Berlin 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, reproduction by photocopying machine or similar means, and storage in data banks. Under § 54 of the German Copyright Law where copies are made for other 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. Printed in Germany. 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 a report by the chairman of the Organizing Committee and a collection of problems. The manuscripts
were typed by Mrs Geary,
done by Mrs Pinkerton, Professor Neumann, Stewart.
the bulk of the bibliographic
and a number of colleagues
Drs Cossey, Kov~cs, McDougall,
work was
helped with proof-reading; Praeger,
Pride, Rangaswamy
and
I here record my thanks to all these people for their lightening of the
editorial burden.
M. F. Newman
CONTENTS
Introduction
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
S.i. Advan, Periodic groups of odd exponent
..................
Reinhold Baer, Einbettungseigenschaften von Normalteilern: Endlichen aufs Unendliche
der Schluss vom 13
. . . . . . . . . . . . . . . . . . . . . . . .
D.W. Barnes, Characterisation of the groups with the GaschHtz cohomology property
63
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Gilbert Baumslag, Finitely presented metabelian groups
............
65
Gilbert Baumslag, Some problems on one-relator groups
............
75
A.J. Ba eye, J. Kautsky and J.W. Wamsley, Computation in nilpotent groups (application)
82
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
90
William W. Boone, Between logic and group theory . . . . . . . . . . . . . . . . Richard Brauer, On the structure of blocks of characters of finite groups A.M. Brunner, Transitivity-systems
of certain one-relator groups
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