Subgroup

A non empty subset H of a group (G, *) is called a subgroup  of G if it is has following properties:

  1. Closure law: If a ϵ H and b ϵ H then a*b ϵ H
  2. Identity law: e ϵ H
  3. Inverse law: If a ϵ H then a-1 ϵ H