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Introduction to Abstract Group Theory

Introduction to Abstract Group Theory. Instructor: Prof. Krishna Hanumanthu, Department of Mathematics, Chennai Mathematical Institute (CMI). This course will introduce abstract groups. We will start with definitions, basic properties and constructions and cover many important theorems in basic group theory, such as Lagrange's theorem, Cauchy's theorem and Sylow theorems. A major emphasis of the course will be to present numerous worked-out examples and problems. A part of the lecture every week will be devoted to explicit calculations. (from nptel.ac.in)

Lecture 05 - Problems 1

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Lecture 01 - Motivational Examples of Groups

Lecture 02 - Definition of a Group and Examples

Lecture 03 - More Examples of Groups

Lecture 04 - Basic Properties of Groups and Multiplication Tables

Lecture 05 - Problems 1

Lecture 06 - Problems 2

Lecture 07 - Problems 3

Lecture 08 - Subgroups

Lecture 09 - Types of Groups

Lecture 10 - Group Homomorphisms and Examples

Lecture 11 - Properties of Homomorphisms

Lecture 12 - Group Isomorphisms

Lecture 13 - Normal Subgroups

Lecture 14 - Equivalence Relations

Lecture 15 - Problems 4

Lecture 16 - Cosets and Lagrange's Theorem

Lecture 17 - S_3 Revisited

Lecture 18 - Problems 5

Lecture 19 - Quotient Groups

Lecture 20 - Examples of Quotient Groups

Lecture 21 - First Isomorphism Theorem

Lecture 22 - Examples and Second Isomorphism Theorem

Lecture 23 - Third Isomorphism Theorem

Lecture 24 - Cauchy's Theorem

Lecture 25 - Problems 6

Lecture 26 - Symmetric Groups I

Lecture 27 - Symmetric Groups II

Lecture 28 - Symmetric Groups III

Lecture 29 - Symmetric Groups IV

Lecture 30 - Odd and Even Permutations I

Lecture 31 - Odd and Even Permutations II

Lecture 32 - Alternating Groups

Lecture 33 - Group Actions

Lecture 34 - Examples of Group Actions

Lecture 35 - Orbits and Stabilizers

Lecture 36 - Counting Formula

Lecture 37 - Cayley's Theorem

Lecture 38 - Problems 7

Lecture 39 - Problems 8 and Class Equation

Lecture 40 - Group Actions on Subsets

Lecture 41 - Sylow Theorem I

Lecture 42 - Sylow Theorem II

Lecture 43 - Sylow Theorem III

Lecture 44 - Problems 9

Lecture 45 - Problems 10