Got this on a home assignment and I don't have a clue...
How do I determine if $\mathbb{Z}_{12}\times\mathbb{Z}_{18}$ and $\mathbb{Z}_{6}\times\mathbb{Z}_{36}$ are isomorphic?
Any hints will be very much appreciated!
2026-03-29 20:12:02.1774815122
Finitely generated abelian groups isomorphism
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You can decompose both groups into cyclic groups of prime power order. This decomposition is unique up to ordering of the factors, so you can decide isomorphy easily having this description at hand.