Exercises in group theory

I. Sets
1.2 Introductory notions
1.2 Mappings
1.3 Binary relations
1.4 MultiplicationII. General algebraic operations
2.1 The notion of algebraic operation
2.2 Basic properties of operations
2.3 Multiplication of subsets
2.4 Homomorphisms
2.5 Semigroups
2.6 Beginning notions of group theoryIII. Composition of maps
3.1 General properties
3.2 Maps with inverses
3.3 Maps with inverses on finite sets
3.4 Endomorphisms
3.5 Groups of motions
3.6 Some particular mapIV. Groups and subgroups
4.1 Coset decomposition
4.2 Conjugacy
4.3 Normal subgroups and factor groups
4.4 Subgroups of finite groups
4.5 Commutators
4.6 Solvable groups
4.7 Nilpotent groups
4.8 Automorphisms of groups
4.9 Transitive permutation groupsV. Defining sets of relations
5.1 In semigroups
5.2 In groups
5.3 Free groups
5.4 Groups given by defining sets of relations
5.5 Free products of groups
5.6 Direct products of groupsVI. Abelian groups
6.1 Simplest properties
6.2 Finite abelian groups
6.3 Finitely generated abelian groups
6.4 Infinite abelian groupsVII. Group representations
7.1 Of general type
7.2 Of transformation groups
7.3 Of matrices
7.4 Groups of homomorphisms of abelian groups
7.5 Characters of groupsVIII. Topological and ordered groups
8.1 Metric spaces
8.2 Groups of continuous transformations of metric space
8.3 Topological spaces
8.4 Topological groups
8.5 Ordered groups.
JOC/EFR August 2007
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