Groups

• Definition and examples
  • Exponent notation
• Order of a group, element
• CYCLIC GROUPS
• SUBGROUPS
• PERMUTATION GROUPS
  • Order of a permutation
  • Products of permutations
  • Finding the inverse permutation
  • Symmetric, Alternating and Permutation groups
  • Cayley's Theorem
• Generating sets
• Cosets
  • Normal subgroups
  • Factor groups
• Homomorphisms
  • Pointers in creating a homomorphism
  • Natural homomorphism
  • Isomorphism
  • Fundamental Theorem of Isomorphism