Can abelian group be infinite?

I'm curious about the concept of abelian groups and their potential to be infinite. Can you elaborate on whether or not an abelian group can indeed be infinite in nature? It's intriguing to ponder the implications of an abelian group that doesn't have a finite number of elements, especially in the context of abstract algebra. Could you provide some insight into this idea, perhaps by discussing examples or properties that may suggest the possibility of an infinite abelian group?