Generators and Relations in Groups and Geometries
Every group is represented in many ways as an epimorphic image of a free group. It seems therefore futile to search for methods involving generators and relations which can be used to detect the structure of a group. Nevertheless, results in the indicated
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NATO ASI Series Advanced Science Institutes Series
A Series presenting the results of activities sponsored by the NA TO Science Committee, which aims at the dissemination of advanced scientific and technological knowledge, with a view to strengthening links between scientific communities. The Series is published by an international board of publishers in conjunction with the NATO Scientific Affairs Division
A LHe Sciences B Physics
Plenum Publishing Corporation London and New York
C Mathematical and Physical Sciences D Behavioural and Social Sciences E Applied Sciences
Kluwer Academic Publishers Dordrecht. Boston and London
F G H I
Springer-Verlag Berlin. Heidelberg. New York. London. Paris and Tokyo Springer-Verlag
Computer and Systems Sciences Ecological Sciences Cell Biology Global Environmental Change
Generators and Relations in Groups and Geometries edited by
A. Barlotti Dipartimento di Matematica "Ulisse Dini", Universitâ degli Studi di Firenze, Florence, Italy
E. W. Ellers Department of Mathematics, University of Toronto, Toronto, Ontario, Canada
P. Plaumann and
K. Strambach Mathematisches Institut, Universităt Erlangen-Nurnberg, Erlangen, F.R.G .
..
Springer-Science+Business Media, BV.
Proceedings of the NATO Advanced Study Institute on Generators and Relations in Groups and Geometries Castelvecchio Pascoli (Lucea), ltaly April1-14, 1990
Llbrary of Congress Cataloglng-In-Publlcatlon Data
ISBN 978-94-010-5496-6 ISBN 978-94-011-3382-1 (eBook) DOI 10.1007/978-94-011-3382-1
Printed on acid-free paper
AII Rights Reserved @ 1991 Springer Science+Business Media Dordrecht
Originally published by Kluwer Academic Publishers in 1991 Softcover reprint ofthe hardcover 1st edition 1991 No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording or by any information storage and retrieval system, without written permission from the copyright owner.
Table of Contents Introduction ..............................................
vii
List of participants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
xiii
Part I 1.1
1.2 1.3
1.4
Optimal factorization of matrices, length problems Classical groups E.W. Ellers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
Generators of automorphism groups of modules H. Ishibashi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
47
Generators of automorphism groups of Cayley algebras H. Lausch ...........................................
69
Products of matrices T.]. Laffey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
95
Part II Reflection geometry II.1 11.2 11.3
Reflection groups - On pre-Hjelmslev groups and related topics F. Knappel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
125
Unitary geometry M. Gotzky .......................... . . . . . . . . .
