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.

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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 :