Learn · Introduction to Group Theory
Lecture 6 of 61Week 2 Properties and the structure of subgroups of a group
Lec 06 - Basic properties of groups.
Prof. R Venkatesh · IISc Bangalore
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- Introduction to Group Theory, IISc Bangalore (at NPTEL)
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All the lectures
- 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.
- 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.
- 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.
- 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
- Lec 20 Some useful definitions
- Lec 21 Internal direct product
- Lec 22 More on normal subgroups
- Lec 23 Normalizer of a subgroup
- 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
- 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
- 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
- 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
- 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
- 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...)
- 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.
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