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Problem. Second Isomorphism Theorem
Suppose that $K$ is a subgroup of $G$ and $N$ is a normal subgroup of $G$. Prove that $K/(K\cap N)\approx KN/N$.
Problem. Third Isomorphism Theorem
Suppose that $M$ and $N$ are normal subgroups of $G$ with $N\leq M$. Prove that $(G/N)/(M/N)\approx G/M$.
Problem. Butterfly Lemma
Later
For more problems, see AllProblems