Infinite Permutation Groups

TL;DR

This lecture course provides an overview of the emerging field of Infinite Permutation Groups, highlighting recent results and Peter Neumann's contributions to the development of this mathematical area.

Contribution

It offers a comprehensive, personal account of the then-new field of Infinite Permutation Groups, including recent results and Neumann's own research insights.

Findings

Most results were new or recently published at the time.

The notes emphasize Neumann's influence and contributions.

The field was established as an independent area in the 1980s.

Abstract

This is a transcript of a lecture course on Infinite Permutation Groups given by Peter M. Neumann (1940-2020) in Oxford during the academic year 1988-1989. The field of Infinite Permutation Groups only emerged as an independent field of study in the 1980's. Most of the results described in these notes were at the time of the lectures brand new and had either just recently appeared in print or had not appeared formally. A large part of the results described is either due to Peter himself or heavily influenced by him. These notes offer Peter's personal take on a field that he was instrumental in creating and in many cases ideas and questions that can not be found in the published literature.