NOC:Introduction to Group Theory

Lecture 1 - Motivation of group theory

Lecture 2 - Definition of a group

Lecture 3 - Examples of groups

Lecture 4 - The symmetric group

Lecture 5 - Subgroups of integers

Lecture 6 - Basic properties of groups

Lecture 7 - Subgroups of a group

Lecture 8 - Subgroup generated by subsets of a group

Lecture 9 - Group of integers modulo n

Lecture 10 - Some elementary number theory - I

Lecture 11 - Some elementary number theory - II

Lecture 12 - Order of an elements in a group

Lecture 13 - Cyclic groups and its subgroups

Lecture 14 - Characterization of cyclic groups

Lecture 15 - Examples of cosets of a subgroup in a group

Lecture 16 - Cosets of a subgroup of a group

Lecture 17 - Lagrange's Theorem

Lecture 18 - Number theoretic applications of Lagrange's Theorem

Lecture 19 - Normal subgroup

Lecture 20 - Some useful definitions

Lecture 21 - Internal direct product

Lecture 22 - More on normal subgroups

Lecture 23 - Normalizer of a subgroup

Lecture 24 - First Isomorphism Theorem

Lecture 25 - Second Isomorphism Theorem

Lecture 26 - Third Isomorphism Theorem

Lecture 27 - Group acting on a set

Lecture 28 - Group action - Examples

Lecture 29 - Isometries of the plane is a group

Lecture 30 - Orthogonal maps

Lecture 31 - Dihedral groups

Lecture 32 - Finite subgroups of the orthogonal group

Lecture 33 - Group acting on a set

Lecture 34 - Group action - Examples

Lecture 35 - Orbit-decomposition Theorem

Lecture 36 - Stabilizer of a subset

Lecture 37 - Applications of group action

Lecture 38 - Class equation

Lecture 39 - Some more applications of group action

Lecture 40 - G-sets and morphisms

Lecture 41 - More examples

Lecture 42 - Burnside's lemma

Lecture 43 - The Sylow's theorems

Lecture 44 - The Sylow's theorems (Continued...)

Lecture 45 - Application of Sylow's Theorems

Lecture 46 - Semidirect product of groups

Lecture 47 - Automorphisms of groups

Lecture 48 - Symmetric and alternating groups

Lecture 49 - Conjugacy in the symmetric group

Lecture 50 - Conjugacy in the symmetric group (Continued...)

Lecture 51 - Simplicity of the alternating groups

Lecture 52 - The sign map

Lecture 53 - The sign map (Continued...)

Lecture 54 - Structure theorem for finite abelian groups (using invariant factors)

Lecture 55 - The structure theorem for finite abelian groups

Lecture 56 - Proof of the structure theorem for finite abelian groups (Continued...)

Lecture 57 - Proof of the structure theorem for finite abelian groups

Lecture 58 - Structure theory of finite abelian p-groups