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

## J.A. Green: *Sets and Groups*

Published $1965$, **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*

- 1.

- 2. Relations
- 1.
*Relations* - 2.
*Equivalence relations* - 3.
*Partitions* - 4.
*Equivalence classes* - 5.
*Congruence of integers* - 6.
*Algebra of congruences**Exercises*

- 1.

- 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*

- 1.

- 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*

- 1.

- 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*

- 1.

- 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*

- 1.

- 7. Homomorphisms
- 1.
*Homomorphisms* - 2.
*Some lemmas on homomorphisms* - 3.
*Isomorphism* - 4.
*Kernel and image* - 5.
*Suggestions for further reading**Exercises*

- 1.

- Tables

- List of Notations

- Answers to Exercises

- Index