# Introduction to Group Theory

- Institution: IISc Bangalore
- Department: Mathematics
- Teacher: Prof. R Venkatesh
- Level: Undergraduate
- Language: English
- Subjects: Mathematics
- Source: [NPTEL](https://nptel.ac.in/courses/111108413)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/111108413)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

## Lectures

1. [Lec 01 - Motivation of group theory](https://invisiblenetwork.ai/learn/nptel/111108413/9d3d7df233d3) (Video)
2. [Lec 02 - Definition of a group.](https://invisiblenetwork.ai/learn/nptel/111108413/e7e33db7d920) (Video)
3. [Lec 03 - Examples of groups.](https://invisiblenetwork.ai/learn/nptel/111108413/a4d72306407f) (Video)
4. [Lec 04 - The symmetric group.](https://invisiblenetwork.ai/learn/nptel/111108413/57b4ad59f35f) (Video)
5. [Lec 05 - Subgroups of integers.](https://invisiblenetwork.ai/learn/nptel/111108413/40a5ae75c8e9) (Video)
6. [Lec 06 - Basic properties of groups.](https://invisiblenetwork.ai/learn/nptel/111108413/90cf7cf0e7ad) (Video)
7. [Lec 07 - Subgroups of a group.](https://invisiblenetwork.ai/learn/nptel/111108413/4ad6bba9baf1) (Video)
8. [Lec 08 - Subgroup generated by subsets of a group](https://invisiblenetwork.ai/learn/nptel/111108413/ab4bc7f7ebad) (Video)
9. [Lec 09 Group of integers modulo n.](https://invisiblenetwork.ai/learn/nptel/111108413/e34651db1d2d) (Video)
10. [Lec 10 Some elementary number theory I.](https://invisiblenetwork.ai/learn/nptel/111108413/d5588a762560) (Video)
11. [Lec 11 Some elementary number theory II.](https://invisiblenetwork.ai/learn/nptel/111108413/9a4c2a1ab63e) (Video)
12. [Lec 12 Order of an elements in a group.](https://invisiblenetwork.ai/learn/nptel/111108413/419b0453d7fd) (Video)
13. [Lec 13 Cyclic groups and its subgroups.](https://invisiblenetwork.ai/learn/nptel/111108413/0c45bd3a97e2) (Video)
14. [Lec 14 Characterization of cyclic groups.](https://invisiblenetwork.ai/learn/nptel/111108413/ac3b8c2a9352) (Video)
15. [Lec 15 Examples of cosets of a subgroup in a group](https://invisiblenetwork.ai/learn/nptel/111108413/cf1e01757e9d) (Video)
16. [Lec 16 Cosets of a subgroup of a group.](https://invisiblenetwork.ai/learn/nptel/111108413/262ac9dab0f7) (Video)
17. [Lec 17 Lagrange’s Theorem.](https://invisiblenetwork.ai/learn/nptel/111108413/99f88bec05de) (Video)
18. [Lec 18 Number theoretic applications of Lagranges Theorem.](https://invisiblenetwork.ai/learn/nptel/111108413/e1ed9ff43715) (Video)
19. [Lec 19 Normal subgroup](https://invisiblenetwork.ai/learn/nptel/111108413/a671c3b14c66) (Video)
20. [Lec 20 Some useful definitions](https://invisiblenetwork.ai/learn/nptel/111108413/b30073fa200e) (Video)
21. [Lec 21 Internal direct product](https://invisiblenetwork.ai/learn/nptel/111108413/7370fa0aea24) (Video)
22. [Lec 22 More on normal subgroups](https://invisiblenetwork.ai/learn/nptel/111108413/a0ca613996b0) (Video)
23. [Lec 23 Normalizer of a subgroup](https://invisiblenetwork.ai/learn/nptel/111108413/12bf335987e6) (Video)
24. [Lec 24 First Isomorphism Theorem](https://invisiblenetwork.ai/learn/nptel/111108413/97b6d5c09172) (Video)
25. [Lec 25 Second Isomorphism Theorem](https://invisiblenetwork.ai/learn/nptel/111108413/1535afdb4522) (Video)
26. [Lec 26 Third Isomorphism Theorem](https://invisiblenetwork.ai/learn/nptel/111108413/7aabff2d0124) (Video)
27. [Lec 27 Group acting on a set](https://invisiblenetwork.ai/learn/nptel/111108413/35cae4f83f77) (Video)
28. [Lec 28 Group action - Examples](https://invisiblenetwork.ai/learn/nptel/111108413/7149f8bbcb75) (Video)
29. [Lec 29 Isometries of the plane is a group](https://invisiblenetwork.ai/learn/nptel/111108413/8b677998e364) (Video)
30. [Lec 30 Orthogonal maps](https://invisiblenetwork.ai/learn/nptel/111108413/6b1ce897f0b4) (Video)
31. [Lec 31 Dihedral groups](https://invisiblenetwork.ai/learn/nptel/111108413/7fb36de5c861) (Video)
32. [Lec 32 Finite subgroups of the orthogonal group](https://invisiblenetwork.ai/learn/nptel/111108413/08a8f4f54d70) (Video)
33. [Lec 33 Group acting on a set](https://invisiblenetwork.ai/learn/nptel/111108413/a391af55f17d) (Video)
34. [Lec 34 Group action - Examples](https://invisiblenetwork.ai/learn/nptel/111108413/cd223773542a) (Video)
35. [Lec 35 Orbit-decomposition Theorem](https://invisiblenetwork.ai/learn/nptel/111108413/639682ca33d3) (Video)
36. [Lec 36 Stabilizer of a subset](https://invisiblenetwork.ai/learn/nptel/111108413/5de72162a0be) (Video)
37. [Lec 37 Applications of group action](https://invisiblenetwork.ai/learn/nptel/111108413/38e28096a0cc) (Video)
38. [Lec 38 Class equation](https://invisiblenetwork.ai/learn/nptel/111108413/e8c351f8403e) (Video)
39. [Lec 39 Some more applications of group action](https://invisiblenetwork.ai/learn/nptel/111108413/8312b61a24f8) (Video)
40. [Lec 40 G-sets and morphisms](https://invisiblenetwork.ai/learn/nptel/111108413/d9e4d55a8e06) (Video)
41. [Lec 41 More examples](https://invisiblenetwork.ai/learn/nptel/111108413/d67bec33d03c) (Video)
42. [Lec 42 Burnside’s lemma](https://invisiblenetwork.ai/learn/nptel/111108413/ea85738b9a41) (Video)
43. [Lec 43 The Sylow’s theorems](https://invisiblenetwork.ai/learn/nptel/111108413/604a9fea74c0) (Video)
44. [Lec 44 The Sylow’s theorems (Continued...)](https://invisiblenetwork.ai/learn/nptel/111108413/3e67ce9316f0) (Video)
45. [Lec 45 Application of Sylow’s Theorems.](https://invisiblenetwork.ai/learn/nptel/111108413/7a7e5ec0923f) (Video)
46. [Lec 46 Semidirect product of groups](https://invisiblenetwork.ai/learn/nptel/111108413/56c0ac853480) (Video)
47. [Lec 47 Automorphisms of groups](https://invisiblenetwork.ai/learn/nptel/111108413/e3dd2e8531bb) (Video)
48. [Lec 48 Symmetric and alternating groups](https://invisiblenetwork.ai/learn/nptel/111108413/eacd8423d4f9) (Video)
49. [Lec 49 Conjugacy in the symmetric group](https://invisiblenetwork.ai/learn/nptel/111108413/e64b9e54a399) (Video)
50. [Lec 50 Conjugacy in the symmetric group (Continued...)](https://invisiblenetwork.ai/learn/nptel/111108413/c87fcff87090) (Video)
51. [Lec 51 Simplicity of the alternating groups](https://invisiblenetwork.ai/learn/nptel/111108413/3967138face8) (Video)
52. [Lec 52 The sign map](https://invisiblenetwork.ai/learn/nptel/111108413/425d61b0fb85) (Video)
53. [Lec 53 The sign map (continued...)](https://invisiblenetwork.ai/learn/nptel/111108413/fbd2d1ac1974) (Video)
54. [Lec 54 Structure theorem for finite abelian groups (using invariant factors).](https://invisiblenetwork.ai/learn/nptel/111108413/765251a5a03a) (Video)
55. [Lec 55 The structure theorem for finite abelian groups](https://invisiblenetwork.ai/learn/nptel/111108413/f135180a6d3c) (Video)
56. [Lec 56 Proof of the structure theorem for finite abelian groups (continued...)](https://invisiblenetwork.ai/learn/nptel/111108413/2315e49808e9) (Video)
57. [Lec 57 Proof of the structure theorem for finite abelian groups](https://invisiblenetwork.ai/learn/nptel/111108413/461448d419c4) (Video)
58. [Lec 58 Structure theory of finite abelian p-groups.](https://invisiblenetwork.ai/learn/nptel/111108413/a979137273ff) (Video)
59. [Live Session 14-03-2024](https://invisiblenetwork.ai/learn/nptel/111108413/9d3d7df233d3-2) (Video)
60. [Live Session 17-03-2025](https://invisiblenetwork.ai/learn/nptel/111108413/e7e33db7d920-2) (Video)
61. [Live Session 15-04-2025](https://invisiblenetwork.ai/learn/nptel/111108413/a4d72306407f-2) (Video)