Order of a group

The order of a group (S, *) is the number of elements of the set S.

The order of a group can be

• finite
  if the set S is composed of a finite number of elements
• infinite
  if the set S is infinite

Example 1

The group (Z, +) is a group of infinite order.

Example 2

The group ({1, -1, i, -i},·) is a finite group of order 4.