# Book:J.A. Green/Sets and Groups

## J.A. Green: Sets and Groups

Published $\text {1965}$, Routledge & Kegan Paul

ISBN 0 7100 4356 2

### 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