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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 21 - First Isomorphism Theorem


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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