# Quick question about subgroups and external direct products

If A and B are groups, then A x B is a group....does the same hold for subgroups? i.e. if A' is a subgroup of A and B' for B, then is A' x B' a subgroup of A x B?

Cheers,
W. =)

## Answers and Replies

Well, does it contain the identity? Is it closed under multiplication (componentwise)? Inverses?