Permutation Groups

1. Front Matter

   Pages i-xii

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2. The Basic Ideas

   • John D. Dixon, Brian Mortimer

   Pages 1-32

3. Examples and Constructions

   • John D. Dixon, Brian Mortimer

   Pages 33-64

4. The Action of a Permutation Group

   • John D. Dixon, Brian Mortimer

   Pages 65-105

5. The Structure of a Primitive Group

   • John D. Dixon, Brian Mortimer

   Pages 106-142

6. Bounds on Orders of Permutation Groups

   • John D. Dixon, Brian Mortimer

   Pages 143-176

7. The Mathieu Groups and Steiner Systems

   • John D. Dixon, Brian Mortimer

   Pages 177-209

8. Multiply Transitive Groups

   • John D. Dixon, Brian Mortimer

   Pages 210-254

9. The Structure of the Symmetric Groups

   • John D. Dixon, Brian Mortimer

   Pages 255-273

10. Examples and Applications of Infinite Permutation Groups

    • John D. Dixon, Brian Mortimer

    Pages 274-301

11. Back Matter

    Pages 302-348

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Permutation Groups form one of the oldest parts of group theory. Through the ubiquity of group actions and the concrete representations which they afford, both finite and infinite permutation groups arise in many parts of mathematics and continue to be a lively topic of research in their own right. The book begins with the basic ideas, standard constructions and important examples in the theory of permutation groups.It then develops the combinatorial and group theoretic structure of primitive groups leading to the proof of the pivotal O'Nan-Scott Theorem which links finite primitive groups with finite simple groups. Special topics covered include the Mathieu groups, multiply transitive groups, and recent work on the subgroups of the infinite symmetric groups. This text can serve as an introduction to permutation groups in a course at the graduate or advanced undergraduate level, or for self- study. It includes many exercises and detailed references to the current literature.

• Algebraic structure
• Group theory
• algebra
• automorphism
• classification
• graphs
• group action

• Department of Mathematics and Statistics, Carleton University, Ottawa, Canada

  John D. Dixon, Brian Mortimer

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