Groups - St Andrews 1981: (Series Number 71 London Mathematical Society Lecture Note Series)

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.

Table of Contents:
Preface; Twenty-five years of Groups St Andrews Conferences C. M. Campbell and E. F. Robertson; Original introduction; 1. An elementary introduction to coset table methods in computational group theory J. Neubüser; 2. Applications of cohomology to the theory of groups D. J. S. Robinson; 3. Groups with exponent four S. J. Tobin; 4. The Schur multiplier: an elementary approach J. Wiegold; 5. A procedure for obtaining simplified defining relations for a subgroup D. G. Arrell, S. Manrai and M. F. Worboys; 6. GLn and the automorphism groups of free metabelian groups and polynomial rings S. Bachmuth and H. Y. Mochizuki; 7. Isoclinisms of group extensions and the Schur multiplicator F. R. Beyl; 8. The maximal subgroups of the Chevalley group G2 (4) G. Butler; 9. Generators and relations for the cohomology ring of Janko's first group in the first twenty-one dimensions G. R. Chapman; 10. The Burnside group of exponent 5 with two generators M. Hall Jr and C. C. Sims; 11. The orientability of subgroups of plane groups A. H. M. Hoare and D. Singerman; 12. On groups with unbounded non-archimedean elements A. H. M. Hoare and D. L. Wilkens; 13. An algorithm for the second derived factor group J. R. Howse and D. L. Johnson; 14. Finiteness conditions and the word problem V. Huber-Dyson; 15. Growth sequences relative to subgroups W. Kimmerle; 16. On the centres of mapping class groups of surfaces C. Maclachlan; 17. A glance at the early history of group rings C. Polcino Milies; 18. Units of group rings: a short survey C. Polcino Milies; 19. Subgroups of small cancellation groups: a survey S. J. Pride; 20. On the hopficity and related properties of some two-generator groups S. J. Pride and A. D. Vella; 21. The isomorphism problem and units in group rings of finite groups K. W. Roggenkamp; 22. On one-relator groups that are free products of two free groups with cyclic amalgamation G. Rosenberger; 23. The algebraic structure of X0-categorical groups J. S. Wilson; 24. Abstracts; 25. Addendum to: 'An elementary introduction to coset table methods in computational group theory' C. M. Campbell, G. Havas and E. F. Robertson; 26. Addendum to: 'Applications of cohomology to the theory of groups' D. J. S. Robinson; 27. Addendum to 'Groups with exponent four' S. J. Tobin; 28. Addendum to 'The Schur multiplier: an elementary approach J. Wiegold.