Let m and n be positive integers. I am asked to Prove that $D_{mn}/ \langle r^m \rangle \cong D_m$.
i belive what i want to do is use the First isomorphism theorem by asking what homomorphism would result in the $\ker \phi =\langle r^m \rangle $ and then looking for the homomorphism.
My question is how do i show that $\langle r^m \rangle$ is a normal subgroup of $D_{mn} $ ?
i managed to do so in a specific example by showing every right coset was equal to a left coset so the subgroup was normal but id like to do it better...( well and for a subgroup of order m.)