Book:Walter Ledermann/Introduction to the Theory of Finite Groups/Fifth Edition

Subject Matter

 * Group Theory

Contents

 * From the Preface of the First Edition (Manchester, May 1948)
 * Preface to the Fourth Edition (Manchester, November 1960)
 * Preface to the Fifth Edition (Brighton, October 1963)


 * $\text {I}$: THE GROUP CONCEPT
 * 1. Introduction
 * 2. The Axioms of Group Theory
 * 3. Examples of Infinite Groups
 * 4. Alternative Axioms for Finite Groups
 * 5. The Multiplication Table
 * 6. Examples of Finite Groups
 * 7. Isomorphic Groups
 * 8. The Order (Period) of an Element
 * 9. Cyclic Groups


 * $\text {II}$: COMPLEXES AND SUBGROUPS
 * 10. The Calculus of Complexes
 * 11. Subgroups
 * 12. Lagrange's Theorem
 * 13. Subgroups of a Cyclic Group
 * 14. Intersection and Generators
 * 15. The Direct Product
 * 16. Survey of Groups up to Order $8$
 * 17. The Product Theorem
 * 18. Decomposition relative to Two Subgroups


 * $\text {III}$: GROUPS OF PERMUTATIONS
 * 19. The Symmetric Group $P_n$
 * 20. Circular Permutations (Cycles)
 * 21. Classes of Permutations
 * 22. Transpositions
 * 23. The Alternating Group $A_n$
 * 24. Cayley's Theorem
 * 25. Transitive Groups
 * 26. Primitive Groups
 * 27. General Remarks about Transformations
 * 28. Groups related to Geometrical Configurations


 * $\text {IV}$: INVARIANT SUBGROUPS
 * 29. Classes of Conjugate Elements
 * 30. Invariant Subgroups
 * 31. The Quotient (Factor) Group
 * 32. The Centre
 * 33. The Commutator Group
 * 34. Homomorphisms and Isomorphisms
 * 35. Automorphisms
 * 36. The Isomorphism Theorems
 * 37. The Jordan-Hölder Composition Theorem
 * 38. Galois' Theorem on the Alternating Group


 * $\text {V}$: SYLOW GROUPS AND PRIME POWER GROUPS
 * 39. A Lemma on Abelian Groups
 * 40. Sylow's Theorems
 * 41. Prime Power Groups


 * $\text {VI}$: ABELIAN GROUPS
 * 42. Additive Notation
 * 43. Finitely Generated Free Abelian Groups
 * 44. Finitely Generated Abelian Groups
 * 45. Invariants and Elementary Divisors


 * $\text {VII}$: GENRATORS AND RELATIONS
 * 46. Finitely Generated and Related Groups
 * 47. Free Groups
 * 48. Relations
 * 49. Definition of Groups





Source work progress
* : Chapter $\text {II}$: Complexes and Subgroups: $10.$ The Calculus of Complexes


 * Some exercises left undone on Chapter $1$.