Can an abelian group be simple?

I'm curious, can an abelian group ever be classified as simple? I understand that a simple group is one that has no non-trivial normal subgroups, but abelian groups are known for their commutative property. Does this characteristic somehow prevent them from being simple, or are there instances where an abelian group can indeed be considered simple? I'm interested in understanding the mathematical principles behind this question and how they apply to the world of algebra and group theory.