Groups - St Andrews 1981

doi:10.1017/CBO9780511661884

This book contains selected papers from the international conference 'Groups - St Andrews 1981', which was held at the University of St Andrews in July/August 1981. Its contents reflect the main topics of the conference: combinatorial group theory; infinite groups; general groups, finite or infinite; computational group theory. Four courses, each providing a five-lecture survey, given by J. Neubuser (Aachen), D. J. S. Robinson (Illinois), S. J. Tobin (Galway) and J. Wiengold (Cardiff), have been expanded into articles, forming the first part of the book. The second part consists of surveys and research articles written by other conference participants. More than two-thirds of the book is composed of survey articles providing a remarkably clear and up-to-date picture of those areas of group theory. The articles which comprise this book, together with their extensive bibliographies, will prove an invaluable tool to researchers in group theory, and, in addition, their detailed expositions make them very suitable for relevant postgraduate courses.

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Contents

Frontmatter
pp i-iv
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Contents
pp v-vii
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Preface
pp viii-viii
- By Colin M. Campbell, St Andrews, August, 2006, Edmund F. Robertson, St Andrews, August, 2006
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Twenty-five years of Groups St Andrews Conferences
pp ix-xii
- By Colin M. Campbell, Edmund F. Robertson
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Original Introduction
pp xiii-xiv
- By Colin M. Campbell, St Andrews, June, 1982, Edmund F. Robertson, St Andrews, June, 1982
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1 - An elementary introduction to coset table methods in computational group theory
pp 1-45
- By J. Neubüser, RWTH Aachen, 5100 Aachen, West Germany
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2 - Applications of cohomology to the theory of groups
pp 46-80
- By D.J.S. Robinson, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, U.S.A.
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3 - Groups with exponent four
pp 81-136
- By S.J. Tobin, University College, Galway, Ireland
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4 - The Schur multiplier: an elementary approach
pp 137-154
- By J. Wiegold, University College, Cardiff, CF1 1XL, Wales
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5 - A procedure for obtaining simplified defining relations for a subgroup
pp 155-159
- By D.G. Arrell, Leeds Polytechnic, Leeds, LS1 3HE, England, S. Manrai, Leeds Polytechnic, Leeds, LS1 3HE, England, M.F. Worboys, Leeds Polytechnic, Leeds, LS1 3HE, England
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6 - GLn and the automorphism groups of free metabelian groups and polynomial rings
pp 160-168
- By S. Bachmuth, University of California, Santa Barbara, CA 93106, U.S.A., H.Y. Mochizuki, University of California, Santa Barbara, CA 93106, U.S.A.
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7 - Isoclinisms of group extensions and the Schur multiplicator
pp 169-185
- By F.R. Beyl, University of Heidelberg, Heidelberg, West Germany
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8 - The maximal subgroups of the Chevalley group G2(4)
pp 186-200
- By G. Butler, University of Sydney, Sydney 2006, N.S.W., Australia
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9 - Generators and relations for the cohomology ring of Janko's first group in the first twenty one dimensions
pp 201-206
- By G.R. Chapman, University of Guelph, Ontario N1G 2W1, Canada
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10 - The Burnside group of exponent 5 with two generators
pp 207-220
- By M. Hall, Jr, California Institute of Technology, Pasadena, CA 91125, U.S.A., C.C. Sims, Rutgers University, New Brunswick, NJ 08903, U.S.A.
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11 - The orientability of subgroups of plane groups
pp 221-227
- By A.H.M. Hoare, University of Birmingham, Birmingham, B15 2TT, England, D. Singerman, University of Southampton, Southampton, S09 5NH, England
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12 - On groups with unbounded non-archimedean elements
pp 228-236
- By A.H.M. Hoare, University of Birmingham, Birmingham, B15 2TT, England, D.L. Wilkens, University of Birmingham, Birmingham, B15 2TT, England
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13 - An algorithm for the second derived factor group
pp 237-243
- By J.R. Howse, University of Nottingham, Nottingham, NG7 2RD, England, D.L. Johnson, University of Nottingham, Nottingham, NG7 2RD, England
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14 - Finiteness conditions and the word problem
pp 244-251
- By V. Huber-Dyson, University of Calgary, Alberta T2N 1N4, Canada
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15 - Growth sequences relative to subgroups
pp 252-260
- By W. Kimmerle, University of Stuttgart, D-7000 Stuttgart-80, West Germany
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16 - On the centres of mapping class groups of surfaces
pp 261-269
- By C. Maclachlan, University of Aberdeen, Aberdeen, AB9 2TY, Scotland
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17 - A glance at the early history of group rings
pp 270-280
- By C. Polcino Milies, University of Sao Paulo, Sao Paulo, Brazil
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18 - Units of group rings: a short survey
pp 281-297
- By C. Polcino Milies, University of São Paulo, São Paulo, Brazil
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19 - Subgroups of small cancellation groups: a survey
pp 298-302
- By S.J. Pride, University of Glasgow, Glasgow, G12 8QW, Scotland
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20 - On the hopficity and related properties of some two-generator groups
pp 303-312
- By S.J. Pride, University of Glasgow, Glasgow G12 8QW, Scotland, A.D. Vella, Oxford Polytechnic, Oxford 0X3 OBP, England
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21 - The isomorphism problem and units in group rings of finite groups
pp 313-327
- By K.W. Roggenkamp, University of Stuttgart, D-7000 Stuttgart-80, West Germany
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22 - On one-relator groups that are free products of two free groups with cyclic amalgamation
pp 328-344
- By G. Rosenberger, University of Dortmund, Dortmund, West Germany
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23 - The algebraic structure of ℵ0-categorical groups
pp 345-358
- By J.S. Wilson, Christ's College, Cambridge, CB2 3BU, England
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24 - Abstracts
pp 359-360
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25 - Addendum to: “An elementary introduction to coset table methods in computational group theory”
pp 361-364
- By Colin M. Campbell, School of Mathematics and Statistics, University of St Andrews, North Haugh, St Andrews, Fife KY16 9SS, Scotland, George Havas, ARC Centre for Complex Systems, School of Information Technology and Electrical Engineering, The University of Queensland, Queensland 4072, Australia, Edmund F. Robertson, School of Mathematics and Statistics, University of St Andrews, North Haugh, St Andrews, Fife KY16 9SS, Scotland
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