# Introduction to Abstract Group Theory

- Institution: Chennai Mathematical Institute
- Department: Mathematics
- Teacher: Prof. Krishna Hanumanthu
- Level: Undergraduate
- Language: English
- Subjects: Mathematics
- Source: [NPTEL](https://nptel.ac.in/courses/111106113)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/111106113)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

This course will introduce abstract groups. We will start with definitions, basic properties and constructions and cover many important theorems in basic group theory, such as Lagrange’s theorem, Cauchy’s theorem and Sylow theorems. A major emphasis of the course will be to present numerous worked-out examples and problems. A part of the lecture every week will be devoted to explicit calculations.

Intended audience: BSc, MSc students studying mathematics

Prerequisites: Any BSc student who is familiar with high school mathematics can take this course

## Lectures

1. [Motivational examples of groups](https://invisiblenetwork.ai/learn/nptel/111106113/74f1fd7a480d) (YouTube)
2. [Definition of a group and examples](https://invisiblenetwork.ai/learn/nptel/111106113/14666c345a58) (YouTube)
3. [More examples of groups](https://invisiblenetwork.ai/learn/nptel/111106113/0c313c58b97a) (YouTube)
4. [Basic properties of groups and multiplication tables](https://invisiblenetwork.ai/learn/nptel/111106113/6de2eb90dfa0) (YouTube)
5. [Problems 1](https://invisiblenetwork.ai/learn/nptel/111106113/b18bbb43a6fc) (YouTube)
6. [Problems 2](https://invisiblenetwork.ai/learn/nptel/111106113/acbac2a4cd26) (YouTube)
7. [Problems 3](https://invisiblenetwork.ai/learn/nptel/111106113/9bd6bb354a01) (YouTube)
8. [Subgroups](https://invisiblenetwork.ai/learn/nptel/111106113/08aecfa3cc30) (YouTube)
9. [Types of groups](https://invisiblenetwork.ai/learn/nptel/111106113/3cc0f50752ea) (YouTube)
10. [Group homomorphisms and examples](https://invisiblenetwork.ai/learn/nptel/111106113/dc37dbbd6b93) (YouTube)
11. [Properties of homomorphisms](https://invisiblenetwork.ai/learn/nptel/111106113/8fc1f18edc95) (YouTube)
12. [Group isomorphisms](https://invisiblenetwork.ai/learn/nptel/111106113/9cb5469f84bd) (YouTube)
13. [Normal subgroups](https://invisiblenetwork.ai/learn/nptel/111106113/0bc6a8671421) (YouTube)
14. [Equivalence relations](https://invisiblenetwork.ai/learn/nptel/111106113/89b037368eab) (YouTube)
15. [Problems 4](https://invisiblenetwork.ai/learn/nptel/111106113/8f2c6b4d1f2f) (YouTube)
16. [Cosets and Lagrange's theorem](https://invisiblenetwork.ai/learn/nptel/111106113/97d3666c1768) (YouTube)
17. [S_3 revisited](https://invisiblenetwork.ai/learn/nptel/111106113/9c7b3c6aa80d) (YouTube)
18. [Problems 5](https://invisiblenetwork.ai/learn/nptel/111106113/9bb6c173636a) (YouTube)
19. [Quotient groups](https://invisiblenetwork.ai/learn/nptel/111106113/6d9f3f314f26) (YouTube)
20. [Examples of quotient groups](https://invisiblenetwork.ai/learn/nptel/111106113/b5d67d2d6ea8) (YouTube)
21. [First isomorphism theorem](https://invisiblenetwork.ai/learn/nptel/111106113/6ba0c6f9c809) (YouTube)
22. [Examples and Second isomorphism theorem](https://invisiblenetwork.ai/learn/nptel/111106113/eaeaaecd6bfa) (YouTube)
23. [Third isomorphism theorem](https://invisiblenetwork.ai/learn/nptel/111106113/2d468f5b3e90) (YouTube)
24. [Cauchy's theorem](https://invisiblenetwork.ai/learn/nptel/111106113/f29de34d8765) (YouTube)
25. [Problems 6](https://invisiblenetwork.ai/learn/nptel/111106113/ea83fd0ba526) (YouTube)
26. [Symmetric groups I](https://invisiblenetwork.ai/learn/nptel/111106113/cb690c1020a8) (YouTube)
27. [Symmetric Groups II](https://invisiblenetwork.ai/learn/nptel/111106113/388ac24cf282) (YouTube)
28. [Symmetric groups III](https://invisiblenetwork.ai/learn/nptel/111106113/0e3f00724ea3) (YouTube)
29. [Symmetric groups IV](https://invisiblenetwork.ai/learn/nptel/111106113/ad31996108da) (YouTube)
30. [Odd and even permutations I](https://invisiblenetwork.ai/learn/nptel/111106113/d50589fc9787) (YouTube)
31. [Odd and even permutations II](https://invisiblenetwork.ai/learn/nptel/111106113/f90a9eb34a25) (YouTube)
32. [Alternating groups](https://invisiblenetwork.ai/learn/nptel/111106113/37f95d8cd398) (YouTube)
33. [Group actions](https://invisiblenetwork.ai/learn/nptel/111106113/f71158bb7de1) (YouTube)
34. [Examples of group actions](https://invisiblenetwork.ai/learn/nptel/111106113/3a3c84d4a610) (YouTube)
35. [Orbits and stabilizers](https://invisiblenetwork.ai/learn/nptel/111106113/53498ca2cac0) (YouTube)
36. [Counting formula](https://invisiblenetwork.ai/learn/nptel/111106113/999e15a62fca) (YouTube)
37. [Cayley's theorem](https://invisiblenetwork.ai/learn/nptel/111106113/7bf417638348) (YouTube)
38. [Problems 7](https://invisiblenetwork.ai/learn/nptel/111106113/e309ec06b6c2) (YouTube)
39. [Problems 8 and Class equation](https://invisiblenetwork.ai/learn/nptel/111106113/ab2364a8fd0a) (YouTube)
40. [Group actions on subsets](https://invisiblenetwork.ai/learn/nptel/111106113/d46a9c0cea76) (YouTube)
41. [Sylow Theorem I](https://invisiblenetwork.ai/learn/nptel/111106113/7ba182282748) (YouTube)
42. [Sylow Theorem II](https://invisiblenetwork.ai/learn/nptel/111106113/039508f28051) (YouTube)
43. [Sylow Theorem III](https://invisiblenetwork.ai/learn/nptel/111106113/e41600ceea0c) (YouTube)
44. [Problems 9](https://invisiblenetwork.ai/learn/nptel/111106113/50ada277a2d0) (YouTube)
45. [Problems 10](https://invisiblenetwork.ai/learn/nptel/111106113/c3f9997fd6ad) (YouTube)