# InfoCoBuild

## 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)

 Motivational Examples of Groups

 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

 References Introduction to Abstract Group Theory Instructor: Prof. Krishna Hanumanthu, Department of Mathematics, Chennai Mathematical Institute (CMI). This course will introduce abstract groups.