====== 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.

{{ :msc:notes:cube-roots-unity-group.jpg?nolink&600|Cube root of unity group}}

  * **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

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  * **Groups_Handwritten_Notes.pdf ~ 4.48 MB**
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  * **Groups_Handwritten_Notes.djvu ~ 3.57 MB**
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====Notes of other subjects====
{{topic>algebra&simplelist}}

{{tag>MSc BS Notes Algebra}}