Book:J.A. Green/Sets and Groups

Subject Matter

 * Abstract Algebra

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