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