# 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.

**Name:**Groups (Handwritten notes)- Lecture Notes**Author:**Atiq ur Rehman**Pages:**82 pages**Format:**PDF and DjVu (see Software section for PDF or DjVu Reader**Size:**PDF: 4.48MB, DjVu: 3.56MB

### CONTENTS OR SUMMARY:

- 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

### Download or View online

**Groups_Handwritten_Notes.pdf ~ 4.48 MB**

**Groups_Handwritten_Notes.djvu ~ 3.57 MB**