Tuesday, 1 October 2013

bijective correspondence involing homomorphsims to a direct product of groups?

bijective correspondence involing homomorphsims to a direct product of
groups?

Let $G$, $G'$ and $H$ be groups. Establish a bijective correspondence
between homomorphisms $\Phi: H \to G \times G'$ from $H$ to the product
group and pairs $(\varphi, \varphi')$ consisting of a homomorphism
$\varphi: H \to G$ and a homomorphism $\varphi': H \to G'$.
I am confused as to what a bijective correspondence is referring to in
this context.

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