NOC:Introduction to Abstract Group Theory

Lecture 1 - Motivational examples of groups

Lecture 2 - Definition of a group and examples

Lecture 3 - More examples of groups

Lecture 4 - Basic properties of groups and multiplication tables

Lecture 5 - Problems - 1

Lecture 6 - Problems - 2

Lecture 7 - Problems - 3

Lecture 8 - Subgroups

Lecture 9 - 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