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
 * External Direct Product Inverses

Closure is trivial.