External direct products are basically n-tuples of elements from different groups.
If
is a collection of groups, the external direct product
is the set of all n – tuples with the ith component is an element of
We can write
and define the product of elements ofas
The product
is done using the group operation of
The direct product of any number of groups is itself a group. If the order of
is m-i then the order ofis 
An obvious example of a direct product is
Each component of
is a real number.
is a group with the group operation being addition, sois a group with the group operation being componentwise addition.
is a group with components first component one of
from 
and the second component one of
from
If all theare abelian, then so is
If theare cyclic of order
respectively, and none of thehave any common factors, then
is cyclic of order