Learn · Introduction to Abstract Group Theory
Lecture 3 of 45Week 1
More examples of groups
Prof. Krishna Hanumanthu · Chennai Mathematical Institute
Credits and licence
- From
- Introduction to Abstract Group Theory, Chennai Mathematical Institute (at NPTEL)
- Licence
- CC BY-NC-SA, as NPTEL states it. Non-commercial use only.
- Attribution
- NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge. Coordinated by IIT Madras.
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- Tweens profiles and older. How courses are placed
All the lectures
- Motivational examples of groups
- Definition of a group and examples
- More examples of groups
- Basic properties of groups and multiplication tables
- Problems 1
- Problems 2
- Problems 3
- Subgroups
- Types of groups
- Group homomorphisms and examples
- Properties of homomorphisms
- Group isomorphisms
- Normal subgroups
- Equivalence relations
- Problems 4
- Cosets and Lagrange's theorem
- S_3 revisited
- Problems 5
- Quotient groups
- Examples of quotient groups
- First isomorphism theorem
- Examples and Second isomorphism theorem
- Third isomorphism theorem
- Cauchy's theorem
- Problems 6
- Symmetric groups I
- Symmetric Groups II
- Symmetric groups III
- Symmetric groups IV
- Odd and even permutations I
- Odd and even permutations II
- Alternating groups
- Group actions
- Examples of group actions
- Orbits and stabilizers
- Counting formula
- Cayley's theorem
- Problems 7
- Problems 8 and Class equation
- Group actions on subsets
- Sylow Theorem I
- Sylow Theorem II
- Sylow Theorem III
- Problems 9
- Problems 10