Course11110841361 lectures
Introduction to Group Theory
Prof. R Venkatesh · IISc Bangalore
Lectures
Week 1 Motivation, definition and first examples of groups.
- Lec 01 - Motivation of group theory
- Lec 02 - Definition of a group.
- Lec 03 - Examples of groups.
- Lec 04 - The symmetric group.
- Lec 05 - Subgroups of integers.
Week 2 Properties and the structure of subgroups of a group
- Lec 06 - Basic properties of groups.
- Lec 07 - Subgroups of a group.
- Lec 08 - Subgroup generated by subsets of a group
- Lec 09 Group of integers modulo n.
- Lec 10 Some elementary number theory I.
Week 3 Elementary theory of numbers and cyclic groups.
- Lec 11 Some elementary number theory II.
- Lec 12 Order of an elements in a group.
- Lec 13 Cyclic groups and its subgroups.
- Lec 14 Characterization of cyclic groups.
Week 4 Cosets of subgroups and normal subgroups
- Lec 15 Examples of cosets of a subgroup in a group
- Lec 16 Cosets of a subgroup of a group.
- Lec 17 Lagrange’s Theorem.
- Lec 18 Number theoretic applications of Lagranges Theorem.
- Lec 19 Normal subgroup
Week 5 Subgroups and products
- Lec 20 Some useful definitions
- Lec 21 Internal direct product
- Lec 22 More on normal subgroups
- Lec 23 Normalizer of a subgroup
Week 6 Isomorphism Theorems, Isometries of the plane
- Lec 24 First Isomorphism Theorem
- Lec 25 Second Isomorphism Theorem
- Lec 26 Third Isomorphism Theorem
- Lec 27 Group acting on a set
- Lec 28 Group action - Examples
Week 7 Isometries of the plane
- Lec 29 Isometries of the plane is a group
- Lec 30 Orthogonal maps
- Lec 31 Dihedral groups
- Lec 32 Finite subgroups of the orthogonal group
Week 8 Group actions (Part 1)
- Lec 33 Group acting on a set
- Lec 34 Group action - Examples
- Lec 35 Orbit-decomposition Theorem
- Lec 36 Stabilizer of a subset
- Lec 37 Applications of group action
Week 9 Group actions (Part 2)
- Lec 38 Class equation
- Lec 39 Some more applications of group action
- Lec 40 G-sets and morphisms
- Lec 41 More examples
- Lec 42 Burnside’s lemma
Week 10 The Sylow’s theorems, semidirect product and automorphisms of groups.
- Lec 43 The Sylow’s theorems
- Lec 44 The Sylow’s theorems (Continued...)
- Lec 45 Application of Sylow’s Theorems.
- Lec 46 Semidirect product of groups
- Lec 47 Automorphisms of groups
Week 11 Symmetric and alternating groups
- Lec 48 Symmetric and alternating groups
- Lec 49 Conjugacy in the symmetric group
- Lec 50 Conjugacy in the symmetric group (Continued...)
- Lec 51 Simplicity of the alternating groups
- Lec 52 The sign map
- Lec 53 The sign map (continued...)
Week 12 Structure theorem for finite abelian groups
- Lec 54 Structure theorem for finite abelian groups (using invariant factors).
- Lec 55 The structure theorem for finite abelian groups
- Lec 56 Proof of the structure theorem for finite abelian groups (continued...)
- Lec 57 Proof of the structure theorem for finite abelian groups
- Lec 58 Structure theory of finite abelian p-groups.
Live Session
Syllabus and materials
At NPTEL, as the course publishes them.
Credits and licence
- Institution
- IISc Bangalore
- Department
- Mathematics
- Teacher
- Prof. R Venkatesh
- Level
- Undergraduate
- Language
- English
- Subjects
- Mathematics
- Source
- NPTEL
- Licence
- CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
- Attribution
- NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
- Who can watch
- NPTEL gives no rating. Invisible Network shows it to Tweens profiles and older, judged from what the source says about it. How courses are placed
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