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

## Walter Ledermann: Introduction to the Theory of Finite Groups (5th Edition)

Published $\text {1964}$, Oliver and Boyd Ltd.

### 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)
chapter $\text {I}$: 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
chapter $\text {II}$: 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
chapter $\text {III}$: 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
28. Groups related to Geometrical Configurations
chapter $\text {IV}$: 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
chapter $\text {V}$: SYLOW GROUPS AND PRIME POWER GROUPS
39. A Lemma on Abelian Groups
40. Sylow's Theorems
41. Prime Power Groups
chapter $\text {VI}$: ABELIAN GROUPS
43. Finitely Generated Free Abelian Groups
44. Finitely Generated Abelian Groups
45. Invariants and Elementary Divisors
chapter $\text {VII}$: GENRATORS AND RELATIONS
46. Finitely Generated and Related Groups
47. Free Groups
48. Relations
49. Definition of Groups
Bibliography
Index

Next

## Source work progress

Some exercises left undone on Chapter $1$.