Hi. Hope someone can help with my problem.

Let G be a group with identity e. If A and B are subgroups of G then, from the Direct Product of Groups Theory, AxB is a subgroup of GxG. Use this result througout.

a) Show that, if A and B are two normal subgroups of G, then AxB is normal subgroup of GxG (Not sure if I am to prove that A and B are two normal subgroups as well as proving AxB is a normal subgroup of GxG).

b) Let H be the subset

H={(g,g):g E G}

Show that H is a subgroup of GxG

Normally I can do these type of questions, it's just the Gx G and AxB bit has confused me a bit.

Thanx