HISTORY AND NOTATION

In the summer of 1988, a London Mathematical Society symposium was held in Durham on “Model Theory and Groups”, organised by Wilfrid Hodges, Otto Kegel and Ileter Neumann. This volume of lecture notes is based on the series of lectures I gave at the symposium, but is something more: since no Proceedings of the symposium was published, I have taken the opportunity to incorporate parts of the talks given by other participants, especially David Evans, Udi Hrushovski, Dugald Macpherson, Ileter Neumann, Simon Thomas and Boris Zil'ber. (A talk by Richard Kaye revealed new horizons to me which I have not fully assimilated; but Richard's own book should appear soon.) In addition, I have made use of parts of the proceedings of the Oxford–QMC seminar on the same subject which ran weekly in 1987–8 and continues once a term (now as the Oxford–QMW seminar!); contributions by Samson Adeleke, Jacinta Covington, Angus Macintyre and John Truss have been especially valuable to me.

Why model theory and groups? In particular, why the special class of permutation groups considered here?

In the middle 1970s, when my interests were entirely finite, John McDermott asked a question about the relationship between transitivity on ordered and unordered n-tuples for infinite permutation groups. The analogous question, and more besides, had been settled for finite permutation groups by Livingstone and Wagner (1965), with techniques which were largely combinatorial and representation-theoretic, and so not likely to be useful here.