Book:László Fuchs/Infinite Abelian Groups/Volume II

László Fuchs: Infinite Abelian Groups, Volume $\text { II }$

Published $\text {1973}$, New York: Academic Press

Continuation of Infinite Abelian Groups, Volume I.

Subject Matter

• Infinite Abelian Groups

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