NOC:Introduction to Abstract Group Theory (USB)

Media Storage Type : 64 GB USB Stick

NPTEL Subject Matter Expert : Prof. Krishna Hanumanthu

NPTEL Co-ordinating Institute : IIT Madras

NPTEL Lecture Count : 45

NPTEL Course Size : 40 GB

NPTEL PDF Text Transcription : Available and Included

NPTEL Subtitle Transcription : Available and Included (SRT)

Lecture Titles:

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