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- #1

- Jan 26, 2012

- 995

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**Problem**: Let $G$ be a group and let $f:G\rightarrow H$ be a group homomorphism. If $U\leq G$, show that $f^{-1}(f(U))=U\ker(f)$.

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**Note**: In this case $f^{-1}$ refers to the

*pre-image*of $f$,

**not**it's

*inverse*!

Remember to read the POTW submission guidelines to find out how to submit your answers!