I would like a little bit of clarification on a basic group theory question:
True or False (Proof or Counterexample): The cosets of the subgroup of rotations R in the dihedral group $D_n$ form a cyclic group via $aR \cdot bR = abR$
My first hunch is to say false somehow because dihedral groups are not always abelian. However, the notation confuses me. From what I understand, in the context of this problem we can consider $D_3$ where "$aR$ " is the set of all "flips/rotations" of the form: (Flip or Rotation)$\cdot$(Rotation).
I'm not necessarily looking for "the answer", I just can't see where the next step might be from here.