(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Given that gcd(n,m)=1, prove that [itex]\mathbb Z_{nm}^\times = \mathbb Z_n^\times \oplus \mathbb Z_m^\times[/itex].

2. Relevant equations

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3. The attempt at a solution

I can prove both groups have the same amount of elements (using Euler's totient function), but I can't figure out how to prove the isomorphism. One way would be to construct the isomorphism, but I can't seem to find one.

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# Homework Help: [abstract algebra] Isomorphic group of units

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