Group whose order is a power of a prime contains an element of order prime
I don't know how to go about this. So the group has elements and I have to somehow use cosets or Langrage's theorem, but I really don't understand much of this. And I can't use Cauchy's Theorem, it uses concepts I haven't covered yet. Any help would be appreciated.
Edit: So I know by Lagrange's theorem that the order of a subgroup of must divide the order of , so given , the cyclic subgroup has order that divides . At this part, I'm stuck.