Wielandt / Booker / Bromley Finite Permutation Groups

1. Auflage 2014
ISBN: 978-1-4832-5829-4
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 124 Seiten, Web PDF

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.

Autoren/Hrsg.

Wielandt, Helmut

Booker, Henry

Bromley, D. Allan

Declaris, Nicholas

Inhaltsverzeichnis

1;Front Cover;1
2;Finite Permutation Groups;4
3;Copyright Page;5
4;Table of Contents;10
5;Preface;8
6;CHAPTER I. FUNDAMENTAL CONCEPTS;12
6.1;§1. Notation;12
6.2;§2. The Transitive Constituents G.;15
6.3;§3. The Subgroups G.;15
6.4;§4. Regular and Semiregular Groups;19
6.5;§5. Frobenius Groups;21
6.6;§6. Blocks;22
6.7;§7. Imprimitive Groups;24
6.8;§8. Primitive Groups;26
7;CHAPTER II. MULTIPLY TRANSITIVE GROUPS;30
7.1;§9. Multiple Transitivity;30
7.2;§10. Multiple Primitivity and Half-Transitivity ;34
7.3;§11. Regular Normal Subgroups of Multiply Transitive Groups;37
7.4;§12. Nonregular Normal Subgroups of Multiply Transitive Groups;41
7.5;§13. Primitive Groups with Transitive Subgroups of Smaller Degree;43
7.6;§14. The Order of Primitive Groups;51
7.7;§15. The Minimal Degree of Multiply Transitive Groups;53
8;CHAPTER III. THE TRANSITIVE CONSTITUENTS OF Ga;55
8.1;§16. Pairing of Constituents of Ga;55
8.2;§17. The Degrees of the Transitive Constituents of Ga;57
8.3;§18. The Structure of the Transitive Constituents of Ga in Primitive Groups G;60
8.4;§19. Transitive Extension;62
9;CHAPTER IV. THE METHOD OF SCHUR;63
9.1;§20. Introduction of Group Elements as Points;63
9.2;§21. Transitivity Modules;65
9.3;§22. Computation in S-Modules;66
9.4;§23. S-Rings;67
9.5;§24. The Relationship between S-Rings and Permutation Groups;71
9.6;§25. Burnside Groups;75
9.7;§26. The Extension Group (H | .1 , .2 , ...);80
9.8;§27. Supplementary Remarks;83
10;CHAPTER V. RELATIONSHIP WITH REPRESENTATION THEORY;89
10.1;§28. The Centralizer Ring;89
10.2;§29. The Reduction of the Permutation Representation;95
10.3;§30. The Degrees of the Irreducible Constituents of a Transitive Permutation Group;100
10.4;§31. Primitive Groups of Degree 2p;104
11;Bibliography;115
12;Author Index;122
13;Notation Used In Text;123
14;Subject Index;124