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Question: If $f\colon G\to H$ is a group homomorphism, and $|G:\mathrm{Ker}(f)|$ and $|H|$ are coprime, then show that $f(G)=1$

Has anyone experienced the ":" notation before? Does it have something to do with cosets? any hints would be greatly appreciated. Thanks for reading.

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    "Modern algebra" was modern some 90 years ago. Nowadays it is just "Algebra" :)2011-03-11

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