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If $K$ and $N$ are subgroups of a group $G$ with $N$ normal in $G$, then $N \trianglelefteq NK$. What is the definition of the homomorphism $K \overset{\subset}{\to} NK$? This is from the proof of the second isomorphism theorem by Hungerford. The full statement is:

The composition $K \overset{\subset}{\to} NK \overset{\pi}{\to} NK/N$ is a homomorphism $f$ with kernel $N \cap K$.

Where $\pi: NK \to NK/N$ given by $a \mapsto aN$ is the canonical epimorphism.

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$K$ is a subgroup of $NK$, so the inclusion $k\in K\mapsto k= 1\cdot k\in NK$ is a group homomorphism (this works for any subgroup of any group). This is what the author calls $K\stackrel{\subset }\to NK$. Another frequent notation is $K\hookrightarrow NK$.

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