Abelian Group

A group (G,*) is said to be abelian if (a*b)=(b*a) ∀a,b∈G

Examples #

• (Z,+): yes
  • We know it’s a group because it follows the properties of closure, associativity, has an identity element and inverse of a number from the set.
  • a+b=b+a ∀a,b∈Z
• (R*,⋅): yes
  • We know it’s a group
  • a*b=b*a ∀a,b∈R