What is the fundamental theorem of abelian groups?
Could you please elaborate on the fundamental theorem of abelian groups? Specifically, how does it relate to the structure and properties of abelian groups? Is there a concise way to summarize its key insights, and how does it help in understanding the behavior of these mathematical structures? I'm particularly interested in how this theorem can be applied in the context of cryptography and blockchain technology, if there are any relevant implications.