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Groups (Handwritten notes)

Name Groups (Handwritten notes)- Lecture Notes
Author(s) 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

Notes of other papers



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