Book:László Fuchs/Infinite Abelian Groups/Volume I

Continued in.

Subject Matter

 * Infinite Abelian Groups

Contents

 * Preface


 * I. Preliminaries
 * 1. Definitions
 * 2. Maps and Diagrams
 * 3. The Most Important Types of Groups
 * 4. Modules
 * 5. Categories of Abelian Groups
 * 6. Functorial Subgroups and Quotient Groups
 * 7. Topologies in Groups
 * Notes


 * II. Direct Sums
 * 8. Direct Sums and Direct Products
 * 9. Direct Summands
 * 10. Pullback and Pushout Diagrams
 * 11. Direct Limits
 * 12. Inverse Limits
 * 13. Completeness and Completions
 * Notes


 * III. Direct Sums of Cyclic Groups
 * 14. Free Abelian Groups&mdash;Defining Relations
 * 15. Finitely Generated Groups
 * 16. Linear Independence and Rank
 * 17. Direct Sums of Cyclic $p$-Groups
 * 18. Subgroups of Direct Sums of Cyclic Groups
 * 19. Countable Free Groups
 * Notes


 * IV. Divisible Groups
 * 20. Divisibility
 * 21. Injective Groups
 * 22. Systems of Equations
 * 23. The Structure of the Divisible Groups
 * 24. The Divisible Hull
 * 25. Finitely Cogenerated Groups
 * Notes


 * V. Pure Subgroups
 * 26. Purity
 * 27. Bounded Pure Subgroups
 * 28. Quotient Groups Modulo Pure Subgroups
 * 29. Pure-Exact Sequences
 * 30. Pure-Projectivity and Pure-Injectivity
 * 31. Generalizations of Purity
 * Notes


 * VI. Basic Subgroups
 * 32. $p$-Basic Subgroups
 * 33. Basic Subgroups of $p$-Groups
 * 34. Further Results on $p$-Basic Subgroups
 * 35. Different $p$-Basic Subgroups
 * 36. Basic Subgroups are Endomorphic Images
 * 37. The Ulm Sequence
 * Notes


 * VII. Algebraically Compact Groups
 * 38. Algebraic Compactness
 * 39. Complete Groups
 * 40. The Structure of Algebraically Compact Groups
 * 41. Pure-Essential Extensions
 * 42. More about Algebraically Compact Groups
 * Notes


 * VIII. Homomorphism Groups
 * 43. Groups of Homomorphisms
 * 44. Exact Sequences for Hom
 * 45. Certain Subgroups for Hom
 * 46. Homomorphism Groups of Torsion Groups
 * 47. Character Groups
 * 48. Duality between Discrete Torsion and $0$-Dimensional Compact Groups
 * Notes


 * IX. Groups of Extensions
 * 49. Group Extensions
 * 50. Extensions as Short Exact Sequences
 * 51. Exact Sequences for Ext
 * 52. Elementary Properties of Ext
 * 53. The Functor Pext
 * 54. Cotorsion Groups
 * 55. The Structure of Cotorsion Groups
 * 56. The Ulm Factors of Cotorsion Groups
 * 57. Applications to Ext
 * 58. Injective Properties of Cotorsion Groups
 * Notes


 * X. Tensor and Torsion Products
 * 59. The Tensor Product
 * 60. Exact Sequences for Tensor Products
 * 61. The Structure of Tensor Products
 * 62. The Torsion Product
 * 63. Exact Sequences for Tor
 * 64. The Structure of Torsion Products
 * Notes


 * Bibliography
 * Table of Notations
 * Author Index
 * Subject Index