Book:László Fuchs/Infinite Abelian Groups: Volume II

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László Fuchs: Infinite Abelian Groups: Volume II

Published $1973$, New York: Academic Press.


Continuation of Infinite Abelian Groups: Volume I.


Subject Matter


Contents

Preface
XI. Separable $p$-Groups
65. Lemmas on $p$-Groups
66. Subsocles
67. Fully Invariant and Large Subgroups
68. Torsion-Complete Groups
69. Further Characterization of Torsion-Complete $p$-Groups
70. Topological Completeness of Torsion-Complete Groups
71. Direct Decompositions of Torsion-Complete Groups
72. The Exchange Property
73. Direct Sums of Torsion-Complete Groups
74. Quasi-Complete Groups
75. Direct Decompositions of $p$-Groups
Notes
XII. $p$-Groups with Elements of Infinite Height
76. Existence Theorems on $p$-Groups
77. Ulm's Theorem
78. Direct Sums of Countable $p$-Groups
79. Nice Subgroups
80. Isotype and Balanced Subgroups
81. $p$-Groups with Nice Composition Series
82. Totally Projective $p$-Groups
83. Simply Presented $p$-Groups
84. Summable $p$-Groups
Notes
XIII. Torsion-Free Groups
85. Torsion-Free Groups of Rank $1$
86. Completely Decomposable Groups
87. Separable Groups
88. Indecomposable Groups
89. Large Indecomposable Groups
90. Direct Decompositions of Finite Rank Groups
91. Direct Decompositions of Countable Groups
92. Quasi-Direct Decomposition
93. Countable Torsion-Free Groups
94. Slender Groups
95. Characterization of Slender Groups by Subgroups
96. Vector Groups
97. Finite-Valued Functions into a Group
98. Homogeneous and Homogeneously Decomposable Groups
99. Whitehead's Problem
Notes
XIV. Mixed Groups
100. Splitting Mixed Groups
101. Baer Groups Are Free
102. Quasi-Splitting Mixed Groups
103. Height-Matrices
104. Mixed Groups of Torsion-Free Rank $1$
105. Groups with Prescribed Ulm Sequences
Notes
XV. Endomorphism Rings
106. Endomorphism Rings
107. Topologies of Endomorphism Rings
108. Endomorphism Rings of Torsion Groups
109. Endomorphism Rings of Separable $p$-Groups
110. Countable Torsion-Free Endomorphism Rings
111. Endomorphism Rings with Special Properties
112. Regular and Generalized Regular Endomorphism Rings
Notes
XVI. Automorphism Groups
113. Groups of Automorphisms
114. Normal Subgroups in Automorphism Groups
115. Automorphism Groups of Torsion Groups
116. Automorphism Groups of Torsion-Free Groups
Notes
XVII. Additive Groups of Rings
117. Subgroups That Are Always Ideals
118. Multiplications on a Group
119. Extensions of Partial Multiplications
120. Torsion Rings
121. Torsion-Free Rings
122. Additive Groups of Artinian Rings
123. Artinian Rings without Quasicyclic Subgroups
124. Additive Groups of Regular and $\pi$-Regular Rings
125. Embeddings in Regular and $\pi$-Regular Rings with Identity
126. Additive Groups of Noetherian Rings and Rings with Restricted Minimum Condition
Notes
XVIII. Groups of Units in Rings
127. Multiplicative Groups of Fields
128. Units of Commutative Rings
129. Groups That Are Unit Groups
Notes
Bibliography
Table of Notations
Author Index
Subject Index