Introduction to Group Theory 1WEPC9G2AR

URI	`m2://res/1WEPC9G2AR`
Kind	course
Creators	R Venkatesh (instructor)
Date	2024-01-17
Scope	in
Ids	course 04dese585:111108413

Expressions

e1: edition

Language	en
Date	2024-01-17

m1: page, IISc Bangalore (record). nptel 111108413
m2: page, 2024-01-17 (record). nptel 111108413

Contents

part 1: Week 1 Motivation, definition and first examples of groups.
session 1: Lec 01 - Motivation of group theory
session 2: Lec 02 - Definition of a group.
session 3: Lec 03 - Examples of groups.
session 4: Lec 04 - The symmetric group.
session 5: Lec 05 - Subgroups of integers.
part 2: Week 2 Properties and the structure of subgroups of a group
session 6: Lec 06 - Basic properties of groups.
session 7: Lec 07 - Subgroups of a group.
session 8: Lec 08 - Subgroup generated by subsets of a group
session 9: Lec 09 Group of integers modulo n.
session 10: Lec 10 Some elementary number theory I.
part 3: Week 3 Elementary theory of numbers and cyclic groups.
session 11: Lec 11 Some elementary number theory II.
session 12: Lec 12 Order of an elements in a group.
session 13: Lec 13 Cyclic groups and its subgroups.
session 14: Lec 14 Characterization of cyclic groups.
part 4: Week 4 Cosets of subgroups and normal subgroups
session 15: Lec 15 Examples of cosets of a subgroup in a group
session 16: Lec 16 Cosets of a subgroup of a group.
session 17: Lec 17 Lagrangeâ€™s Theorem.
session 18: Lec 18 Number theoretic applications of Lagranges Theorem.
session 19: Lec 19 Normal subgroup
part 5: Week 5 Subgroups and products
session 20: Lec 20 Some useful definitions
session 21: Lec 21 Internal direct product
session 22: Lec 22 More on normal subgroups
session 23: Lec 23 Normalizer of a subgroup
part 6: Week 6 Isomorphism Theorems, Isometries of the plane
session 24: Lec 24 First Isomorphism Theorem
session 25: Lec 25 Second Isomorphism Theorem
session 26: Lec 26 Third Isomorphism Theorem
session 27: Lec 27 Group acting on a set
session 28: Lec 28 Group action - Examples
part 7: Week 7 Isometries of the plane
session 29: Lec 29 Isometries of the plane is a group
session 30: Lec 30 Orthogonal maps
session 31: Lec 31 Dihedral groups
session 32: Lec 32 Finite subgroups of the orthogonal group
part 8: Week 8 Group actions (Part 1)
session 33: Lec 33 Group acting on a set
session 34: Lec 34 Group action - Examples
session 35: Lec 35 Orbit-decomposition Theorem
session 36: Lec 36 Stabilizer of a subset
session 37: Lec 37 Applications of group action
part 9: Week 9 Group actions (Part 2)
session 38: Lec 38 Class equation
session 39: Lec 39 Some more applications of group action
session 40: Lec 40 G-sets and morphisms
session 41: Lec 41 More examples
session 42: Lec 42 Burnsideâ€™s lemma
part 10: Week 10 The Sylow’s theorems, semidirect product and automorphisms of groups.
session 43: Lec 43 The Sylowâ€™s theorems
session 44: Lec 44 The Sylowâ€™s theorems (Continued...)
session 45: Lec 45 Application of Sylowâ€™s Theorems.
session 46: Lec 46 Semidirect product of groups
session 47: Lec 47 Automorphisms of groups
part 11: Week 11 Symmetric and alternating groups
session 48: Lec 48 Symmetric and alternating groups
session 49: Lec 49 Conjugacy in the symmetric group
session 50: Lec 50 Conjugacy in the symmetric group (Continued...)
session 51: Lec 51 Simplicity of the alternating groups
session 52: Lec 52 The sign map
session 53: Lec 53 The sign map (continued...)
part 12: Week 12 Structure theorem for finite abelian groups
session 54: Lec 54 Structure theorem for finite abelian groups (using invariant factors).
session 55: Lec 55 The structure theorem for finite abelian groups
session 56: Lec 56 Proof of the structure theorem for finite abelian groups (continued...)
session 57: Lec 57 Proof of the structure theorem for finite abelian groups
session 58: Lec 58 Structure theory of finite abelian p-groups.
part 13: Live Session
session 59: Live Session 14-03-2024
session 60: Live Session 17-03-2025
session 61: Live Session 15-04-2025

Catalogue records

nptel: 111108413 (manifestation)
nptel_video: 111108413 (manifestation)