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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.
Chapter I Fundamental Concepts
2. The Transitive Constituents G△
3. The Subgroups G△
4. Regular and Semiregular Groups
5. Frobenius Groups
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
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
Notation Used in Text
- No. of pages:
- © Academic Press 1964
- 1st January 1964
- Academic Press
- eBook ISBN:
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