Oligomorphic Permutation Groups

Peter J. Cameron (Author)

9780521388368, Cambridge University Press

Paperback, published 29 June 1990

172 pages
22.8 x 15.2 x 1.3 cm, 0.29 kg

' … a very attractive textbook for any student interested in discrete mathematics.' International Mathematical News

The study of permutation groups has always been closely associated with that of highly symmetric structures. The objects considered here are countably infinite, but have only finitely many different substructures of any given finite size. They are precisely those structures which are determined by first-order logical axioms together with the assumption of countability. This book concerns such structures, their substructures and their automorphism groups. A wide range of techniques are used: group theory, combinatorics, Baire category and measure among them. The book arose from lectures given at a research symposium and retains their informal style, whilst including as well many recent results from a variety of sources. It concludes with exercises and unsolved research problems.

1. Introduction
2. Preliminaries
3. Examples and growth rates
4. Subgroups
5. Miscellaneous topics.

Subject Areas: Mathematical logic [PBCD]