Book:J.A. Green/Sets and Groups
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J.A. Green: Sets and Groups
Published $\text {1965}$, Routledge & Kegan Paul
- ISBN 0 7100 4356 2
Subject Matter
Contents
- Preface
- 1. Sets
- 1. Sets
- 2. Subsets
- 3. Intersection
- 4. Union
- 5. The algebra of sets
- 6. Difference and complement
- 7. Pairs. Product of sets
- 8. Sets of sets
- Exercises
- 2. Relations
- 1. Relations
- 2. Equivalence relations
- 3. Partitions
- 4. Equivalence classes
- 5. Congruence of integers
- 6. Algebra of congruences
- Exercises
- 3. Mappings
- 1. Mappings
- 2. Equality of mappings
- 3. Injective, surjective, bijective; inverse mappings
- 4. Product of mappings
- 5. Identity mappings
- 6. Products of bijective mappings: permutations
- 7. Similarity
- Exercises
- 4. Groups
- 1. Binary operations on a set
- 2. Commutative and associative operations
- 3. Units and zeros
- 4. Gruppoids, semigroups and groups
- 5. Examples of groups
- 6. Elementary theorems on groups
- Exercises
- 5. Subgroups
- 1. Subsets closed to an operation
- 2. Subgroups
- 3. Subgroup generated by a subset
- 4. Cyclic groups
- 5. Groups acting on sets
- 6. Stabilizers
- Exercises
- 6. Cosets
- 1. The quotient sets of a subgroup
- 2. Mappings of quotient sets
- 3. Index. Transversals
- 4. Lagrange's theorem
- 5. Orbits
- 6. Normal subgroups
- 7. Quotient groups
- Exercises
- 7. Homomorphisms
- 1. Homomorphisms
- 2. Some lemmas on homomorphisms
- 3. Isomorphism
- 4. Kernel and image
- 5. Suggestions for further reading
- Exercises
- Tables
- List of Notations
- Answers to Exercises
- Index
Cited by
Sources
- 1969: C.R.J. Clapham: Introduction to Abstract Algebra ... (next): Preface