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Problem 101 (Homomorphisms Preserve Normal Subgroups)

Suppose that $f:G\to H$ is a homomorphism. Use The Normal Subgroup Test to prove the following:

  1. If $N$ is normal in $G$, then $f(N)$ is normal in $f(G)$.
  2. If $B$ is normal in $H$, then $f^{-1}(B)$ is normal in $G$.

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