Order (group theory)

Cardinality of a mathematical group, or of the subgroup generated by an element

The relationship between the two concepts of order is the following: if we write

As an immediate consequence of the above, we see that the order of every element of a group divides the order of the group. For example, in the symmetric group shown above, where ord(S3) = 6, the possible orders of the elements are 1, 2, 3 or 6.