Infinite permutation groups

A “new” publication by Peter Neumann has just appeared on the arXiv: the notes of a 48-lecture course he gave in Oxford in the academic year 1988–89 on infinite permutation groups, compiled and edited by David Craven, Dugald Macpherson and Röggi Möller. The link is here.

The notes are divided into three parts, corresponding to the three terms of the Oxford academic year. In Michaelmas, we have history, basics about permutation groups, and properties of infinite symmetric groups (including the small index subgroups) and the automorphism groups of the rational line. Hilary brings us imprimitivity and wreath products, primitivity and orbital graphs, and theorems about groups with all suborbits finite, and finitary and bounded permutation groups. Then in Trinity we have highly homogeneous groups and Jordan groups.

Those who know Peter’s work will recognise that he has included many of his own pioneering results. The addition of “Infinite permutation groups” to the MSC subject list is due in no small part to Peter’s work.

I cannot think of a text better suited for someone who is about to start research on infinite permutation groups. Of course not everything is covered but the notes provide an excellent grounding. We all owe thanks to the three editors for the work they have put in on this project.