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Second isomorphism theorem (page 214)
Problem.
If $K$ is a subgroup of $G$ and $N$ is a normal subgroup of $G$, then $K/(K\cap N)$ is isomorphic to $KN/N$.
Third Isomorphism Theorem (page 214)
Problem.
If $M$ and $N$ are normal subgroups of $G$ with $N\leq M$, then $(G/N)/(M/N)\approx(G/M)$
Problem
Do we know that $(G\times H)/H\approx G$? Do we know that $(GH)/H\approx G$? When do we know $(G/H)\times H\approx G$? We need a visual of what each of these concepts mean. Does expanding a group and then collapsing the expansion out always result in what you started with.
For more problems, see AllProblems