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Oligomorphic Permutation Groups

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.
Oligomorphic Permutation Groups
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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.
Peter Cameron has taught mathematics at Oxford University and Queen Mary, University of London, with shorter spells at other institutions. He has received the Junior Whitehead Prize of the London Mathematical Society, and the Euler Medal of the Institute of Combinatorics and its Applications, and is
currently chair of the British Combinatorial Committee.
1. Introduction; 2. Preliminaries; 3. Examples and growth rates; 4. Subgroups; 5. Miscellaneous topics.
' ... a very attractive textbook for any student interested in discrete mathematics.' International Mathematical News
Author
Peter J. Cameron
Short Title
OLIGOMORPHIC PERMUTATION GROUP
Pages
172
Publisher
Cambridge University Press
Series
Cambridge Studies in Philosophy
Language
English
ISBN-10
0521388368
ISBN-13
9780521388368
Media
Book
Format
Paperback
DEWEY
512.2
Series Number
152
Year
1990
Publication Date
1990-06-30
Imprint
Cambridge University Press
Place of Publication
Cambridge
Country of Publication
United Kingdom
Residence
US
Illustrations
black & white illustrations
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