I have an exam type question on subgroups/index, but I am completely lost on what to do as I don't really understand the whole idea of cosets:
If G is a finite group with subgroups H and Z, show that:
$[G:H\cap Z]=[G:H]\cdot[H:H\cap Z]\leq [G:H]\cdot[G:Z]$ $\\$
Any help would be greatly appreciated. Thanks