Introduction

Throughout the second week of the Groups '93 meeting a workshop on Computational Group Theory (CGT for short) took place. The underlying mathematical methods were described in four series of lectures (‘Finitely Presented Groups’, ‘Collection Methods’, ‘Permutation Groups’, ‘Representations’) and three single lectures (‘Cohomology Groups’, ‘Matrix Groups’, ‘Groups, Graphs and Designs’). The practical aspect was present in a lecture ‘Introduction to GAP’, a course ‘Programming in GAP’ and exercises using GAP during the afternoons. It is a pleasure to thank the large number of colleagues who helped running this workshop.

During the first week, I gave a plenary talk which had the same title as this paper. It had the dual function to give information on the plan and intention of the workshop, but also in a wider sense to discuss the present state of CGT and its role in group theory at large. In parts the talk reflected rather personal viewpoints. Since in that it differs from papers normally read in a conference, I had doubts, if it should at all go into the proceedings. The editors have encouraged me to write it up, so here it is, much in the form of the talk delivered.

CGT may be described as comprising the development, analysis, implementation and use of group theoretical algorithms. The first two depend on and draw from the corresponding part of group theory and hence teaching the methods of CGT is best organized following the lines of the theory – it definitely was organized that way in our workshop.