- Thread starter
- Moderator
- #1
- Jan 26, 2012
- 995
Here's this week's problem.
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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!
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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 $f^{-1}(f(U))=U\ker(f)$.
-----
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!