Let the homomorphism $f:H \rtimes K \rightarrow K$ be defined by $f(hk)=k$.
Now, I will construct the homomorphism $f: [H \rtimes K ,H \rtimes K ] \rightarrow [K,K]$. How to find the kernel of $f$?. Is the kernel isomorphic with $[H,H]$?
Let the homomorphism $f:H \rtimes K \rightarrow K$ be defined by $f(hk)=k$.
Now, I will construct the homomorphism $f: [H \rtimes K ,H \rtimes K ] \rightarrow [K,K]$. How to find the kernel of $f$?. Is the kernel isomorphic with $[H,H]$?