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FINITE GROUP THEORY (M2, Kaplansky)
Lecture Topic : FINITE GROUP THEORY (M2, Kaplansky)
Prerequisites : Finite Group Theory (M1); Abstract Algebra (M1);
Recommended Text(s) :
“Infinite Abelian Groups”, Irving Kaplansky,UniversityofMichiganPress, 1954.
Approx price new on Amazon.com (hard copy) : –
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eMule search key word(s) : Kaplansky, Infinite Abelian Groups
Lectures and Links :
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Lecture 1 (link)
Ch.1 Introduction
Ch.2 Examples of Abelian Groups
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Lecture 2 (link)
Ch.3 Torsion Groups
Ch.4 Zorn’s Lemma
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Lecture 3 (link)
Ch.5 Divisible Groups
Ch.6 Three Test Problems
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Lecture 4 (link)
Ch.7 Pure Subgroups
Ch.8 Groups of Bounded Order
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Lecture 5 (link)
Ch.9 Height
Ch.10 Direct Sums of Cyclic Groups
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Lecture 6 (link)
Ch.11 Ulm’s Theorem
Ch.12 Modules and Linear Transformations
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Lecture 7 (link)
Ch.13 Banach Spaces
Ch.14 Valuation Rings
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Lecture 8 (link)
Ch.15 Torsion-Free Modules
Ch.16 Complete Modules
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Lecture 9 (link)
Ch.17 The Algebraic Structure of Compact Abelian Groups
Ch.18 Characteristic Submodules
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Lecture 10 (link)
Ch.19 The Ring of Endomorphisms
Ch.20 Guide to the Literature
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Links to Other Lecturers on this Topic :