# Normal Subgroups

Please see the attached file for the fully formatted problem.

Let G be a group and let D ={(a,a,a):a E G}. Prove that D is a normal subgroup of G+G+G if and only if G is Abelian.

Â© BrainMass Inc. brainmass.com February 24, 2021, 2:17 pm ad1c9bdddfhttps://brainmass.com/math/linear-algebra/normal-subgroup-functions-11841

#### Solution Preview

Please see the attached file for the complete solution.

Thanks for using BrainMass.

Proof:

First, I claim . ...

#### Solution Summary

A normal subgroup is investigated. The proof is elegant.

$2.19