External Direct Product of Groups is Group

Theorem
The external direct product of a sequence of groups is itself a group.

The external direct product of a sequence of abelian groups is itself an abelian group.

Proof
Follows directly from the generalized results of:
 * External Direct Product Associativity;
 * External Direct Product Commutativity;
 * External Direct Product Identity, and
 * External Direct Product Inverses.

Closure is trivial.