Finite Permutation Groups

Finite Permutation Groups provides an introduction to the basic facts of both the theory of abstract finite groups and the theory of permutation groups. This book deals with older theorems on multiply transitive groups as well as on simply transitive groups.

Organized into five chapters, this book begins with an overview of the fundamental concepts of notation and Frobenius group. This text then discusses the modifications of multiple transitivity and can be used to deduce an improved form of the classical theorem. Other chapters consider the concept of simply transitive permutation groups. This book discusses as well permutation groups in the framework of representation theory. The final chapter deals with Frobenius' theory of group characters.

This book is a valuable resource for engineers, mathematicians, and research workers. Graduate students and readers who are interested in finite permutation groups will also find this book useful.

Preface

Chapter I Fundamental Concepts

1. Notation

2. The Transitive Constituents G△

3. The Subgroups G△

4. Regular and Semiregular Groups

5. Frobenius Groups

6. Blocks

7. Imprimitive Groups

8. Primitive Groups

Chapter II Multiply Transitive Groups

9. Multiple Transitivity

10. Multiple Primitivity and Half-Transitivity

11. Regular Normal Subgroups of Multiply Transitive Groups

12. Nonregular Normal Subgroups of Multiply Transitive Groups

13. Primitive Groups with Transitive Subgroups of Smaller Degree

14. The Order of Primitive Groups

15. The Minimal Degree of Multiply Transitive Groups

Chapter III The Transitive Constituents of Gα

16. Pairing of Constituents of Gα

17. The Degrees of the Transitive Constituents of Gα

18. The Structure of the Transitive Constituents of Gα in Primitive Groups G

19. Transitive Extension

Chapter IV The Method of Schur

20. Introduction of Group Elements as Points

21. Transitivity Modules

22. Computation in S-Modules

23. S-Rings

24. The Relationship between S-Rings and Permutation Groups

25. Burnside Groups

26. The Extension Group (H | ξ1,ξ2,···)

27. Supplementary Remarks

Chapter V Relationship with Representation Theory

28. The Centralizer Ring

29. The Reduction of the Permutation Representation

30. The Degrees of the Irreducible Constituents of a Transitive Permutation Group

31. Primitive Groups of Degree 2p

Bibliography

Author Index

Notation Used in Text

Subject Index