Author | Lyapin, E. S. author |
---|---|
Title | Exercises in Group Theory [electronic resource] / by E. S. Lyapin, A. Ya. Aizenshtat, M. M. Lesokhin |
Imprint | Boston, MA : Springer US, 1972 |
Connect to | http://dx.doi.org/10.1007/978-1-4613-4589-3 |
Descript | XIV, 240 p. online resource |
1 Sets -- 1. Basic Concepts -- 2. Mappings of Sets -- 3. Binary Relations -- 4. Multiplication of Binary Relations -- 2 Algebraic Operations of a General Type -- 1. The Concept of an Algebraic Operation -- 2. Basic Properties of Operations -- 3. Multiplication of Subsets of a Multiplicative Set -- 4. Homomorphisms -- 5. Semigroups -- 6. Elementary Concepts of the Theory of Groups -- 3 Compositions of Transformations -- 1. General Properties of the Composition of Transformations -- 2. Invertible Transformations -- 3. Invertible Transformations of Finite Sets -- 4. Endomorphisms -- 5. Groups of Isometries -- 6. Partial Transformations -- 4 Groups and Their Subgroups -- 1. Decomposition of a Group by a Subgroup -- 2. Conjugate Classes -- 3. Normal Subgroups and Factor Groups -- 4. Subgroups of Finite Groups -- 5. Commutators and the Commutator Subgroup -- 6. Solvable Groups -- 7. Nilpotent Groups -- 8. Automorphisms of Groups -- 9. Transitive Groups of Transformations -- 5 Defining Sets of Relations -- 1. Defining Sets of Relations on Semigroups -- 2. Defining Sets of Relations on Groups -- 3. Free Groups -- 4. Groups Defined by Sets of Relations -- 5. Free Products of Groups -- 6. The Direct Product of Groups -- 6 Abelian Groups -- 1. Elementary Properties of Abelian Groups -- 2. Finite Abelian Groups -- 3. Finitely Generated Abelian Groups -- 4. Infinite Abelian Groups -- 7 Group Representations -- 1. Representations of a General Type -- 2. Representations of Groups by Transformations -- 3. Representations of Groups by Matrices -- 4. Groups of Homomorphisms of Abelian Groups -- 5. Characters of Groups -- 8 Topological and Ordered Groups -- 1. Metric Spaces -- 2. Groups of Continuous Transformations of a Metric Space -- 3. Topological Spaces -- 4. Topological Groups -- 5. Ordered Groups -- Hints -- 1 -- 2 -- 3 -- 4 -- 5 -- 6 -- 7 -- 8 -- Answers -- 1 -- 2 -- 3 -- 4 -- 5 -- 6 -- 7 -- 8