I was solving an exercise which asked to determine all abelian groups of order 48 two by two not isomorphic with each other and it seemed natural to me to use in the process the following proposition: $$ \Bbb{N}_a\times\Bbb{N}_b \simeq \Bbb{N}_{ab} \iff MCD(a,b)=1$$ I looked up in my notes but I have not properly found an answer to this although I believe it comes from the Chinese Remainder Theorem; can someone tell me if it's true and if it is explain me why it is? Thanks!
2026-03-29 18:48:58.1774810138
Isomorphisms between cyclic groups
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