MODULE 2 and 3

• Groups


  sets of one-to-one functions on finite sets that could be grouped together to form a set closed under composition.
• 3 Properties of a Group

  1. Associativity
  2. Existence of Identity Element
  3. For every element, there is an inverse
• Abelian Group


  If the group's binary operation * is commutative.
• Infinite Groups


  are groups where set G has infinite number of elements,
• Order of groups


  The number of elements of a group
• Cyclic Group


  there is some element a in G that generates G.
• What is the generator/s of z4?

  <1,3>
• Find the generator/s of U10

  <3,7>
• Find the remainder of (7)^30

  9