Is abelian group closed?

Excuse me, could you please clarify something for me? The paragraph mentions the term "abelian group," and I'm wondering if it is indeed closed. By closed, I mean does the set of elements within the abelian group satisfy the property that for any two elements in the group, their operation results in another element that is also within the group? I'm asking because I'm trying to understand the fundamental properties of abelian groups and how they relate to other algebraic structures.