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Abelian groups /
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Oxford ; New York :
Pergamon Press,
[1967, �1960]
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| Edición: | [3rd ed.]. |
| Colección: | International Series of Monographs in Pure and Applied Mathematics, V.12.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Front Cover; Abelian Groups; Copyright Page; PREFACE; Table of Contents; TABLE OF NOTATIONS; CHAPTER I. BASIC CONCEPTS. THE MOST IMPORTANT GROUPS; 1. Notation and terminology; 2. Direct sums; 3. Cyclic groups; 4. Quasicyclic groups; 5. The additive group of the rationals; 6. The p-adic integers; 7. Operator modules; 8. Linear independence and rank; Exercises; CHAPTER II. DIRECT SUM OF CYCLIC GROUPS; 9. Free (abelian) groups; 10. Finite and finitely generated groups; 11. Direct sums of cyclic p-groups; 12. Subgroups of direct sums of cyclic groups; 13. Two dual criteria for the basis.
- 14. Further criteria for the existence of a basisExercises; CHAPTER III. DIVISIBLE GROUPS; 15. Divisibility by integers in groups; 16. Homomorphisms into divisible groups; 17. Systems of linear equations over divisible groups; 18. The direct summand property of divisible groups; 19. The structure theorem on divisible groups; 20. Embedding in divisible groups; Exercises; CHAPTER IV. DIRECT SUMMANDS AND PURE SUBGROUPS; 21. Direct summands; 22. Absolute direct summands; 23. Pure subgroups; 24. Bounded pure subgroups; 25. Factor groups with respect to pure subgroups.
- 26. Algebraically compact groups27. Generalized pure subgroups; 28. Neat subgroups; Exercises; CHAPTER V. BASIC SUBGROUPS; 29. Existence of basic subgroups. The quasibasis; 30. Properties of basic subgroups; 31. Different basic subgroups of a group; 32. The basic subgroup as an endomorphic image; Exercises; CHAPTER VI. THE STRUCTURE OF p-GROUPS; 33. p-groups without elements of infinite height; 34. Closed p-groups; 35. The Ulm sequence; 36. Zippin's theorem; 37. Ulm's theorem; 38. Construction of groups with a prescribed Ulm sequence; 39. Non-isomorphic groups with the same Ulm sequence.
- 40. Some applications41. Direct decompositions of p-groups; Exercises; CHAPTER VII. TORSION FREE GROUPS; 42. The type of elements. Groups of rank 1; 43. Indecomposable groups; 44. Torsion free groups over the p-adic integers; 45. Countable torsion free groups; 46. Completely decomposable groups; 47. Complete direct sums of infinite cyclic groups. Slender groups; 48. Homogeneous groups; 49. Separable groups; Exercises; CHAPTER VIII. MIXED GROUPS; 50. Splitting mixed groups; 51. Factor groups of free groups; 52. A characterization of arbitrary groups by matrices.
- 53. Groups over the p-adic integersExercises; CHAPTER IX. HOMOMORPHISM GROUPS AND ENDOMORPHISM RINGS; 54. Homomorphism groups; 55. Endomorphism rings; 56. The endomorphism ring of p-groups; 57. Endomorphism rings with special properties; 58. Automorphism groups; 59. Fully invariant subgroups; Exercises; CHAPTER X. GROUP EXTENSIONS; 60. Extensions of groups; 61. The group of extensions; 62. Induced endomorphisms of the group of extensions; 63. Structural properties of the group of extensions; Exercises; CHAPTER XI. TENSOR PRODUCTS; 64. The tensor product; 65. The structure of tensor products.