1. ## Group Axioms Help

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)

2. Originally Posted by moolimanj
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.
$GG=G$ thus $AB$ being a subgroup of $GG$ means $AB$ is subgroup of $G$. But that is not true. If one of $A,B$ is normal then it is true. In general it is not.