Hi all

If G is a group with identity e and if A and B and subgroups of G then A*B is a subgroup of G*G.

How do I use this to show that if A and B are two normal subgroups of G, then A*B is a normal subgroup of G*G?

Also, if H is the subset H={(g,g):gEG} how do i show that H is a subgroup of G*G?

Thanks again - and sorry for the previous posts around groups and geometry (not my strongest subjects)