Book:László Fuchs/Infinite Abelian Groups: Volume I

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László Fuchs: Infinite Abelian Groups: Volume I

Published $1970$, New York: Academic Press.


Continued in Infinite Abelian Groups: Volume II.


Subject Matter


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—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