Prove or disprove the following assertion. Let $G, H,$ and $K$ be groups. If $G\times K \cong H \times K$, then $G\cong H$.
Cancellation Law for External direct product
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abstract-algebra
group-theory
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0I'm voting to close this question as off-topic because use shows no effort to solve – 2017-03-01
1 Answers
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What if $G = \mathbb Z$, $H = \mathbb Z \oplus \mathbb Z$ and $K$ is direct sum of countably many copies of $\mathbb Z$?