Groups (Handwritten Notes) by Atiq ur Rehman

Groups are a basic idea in algebra, introduced in high school. It's a very interesting topic in math.

Cube root of unity group

Groups; definition and examples
Order of group, order of element
Periodic group, mixed group
Subgroup
Invalution
Relation between groups, homomorphism, monomorphism, epimorphism, isomorphism, endomorphism, examples and related theorem
Kernel, definition and related theorems
Cyclic group, related theorems
Complex in a group, product of complexes and related theorems
Coset, definition and examples
Index of subgroup, Lagrange's theorem
Double coset, related theorem
Normalizer, definition and related theorems
Centralizer, centre of group, related theorem
Conjugate or transform of a group, definition and related theorems
Self conjugate, conjugancy class, related theorem
Class equation, p-group, definition and related theorems
Conjugate subgroup, definition and related theorems
Normal subgroup, definition and related theorems
Factor or quotient group, definition and related theorem
1st isomorphism theorem, related theorem
2nd isomorphism theorem
3rd isomorphism theorem
Endomorphism, automorphism, definition and related theorem
Conjugation as an automorphism
Inner and outer automorphism, definition and related theorems
Commutator of a group, definition and related theorem
Derive group or commutative group, definition and related theorem
Direct product of groups, definition and related theorems
Invariant subgroup
Characteristic subgroup

Groups_Handwritten_Notes.pdf ~ 4.48 MB
- DWN Link 1: Direct Link
- DWN Link 2: mediafire.com

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