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Problem 89 (The order of $a$ is a multiple of the order of $f(a)$, or $|a|=k|f(a)|$)
Suppose that $f:G\to H$ is a homomorphism. Prove that if $a\in G$ has order $n$, show that $|f(a)|$ divides $n$, i.e. show that $|a|$ is a multiple of $|f(a)|$.
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