1. The problem statement, all variables and given/known data Any help with this question would be great: G is a group such that |G| = pk, p is prime and k is a positive integer. Show that G must have an element of order p. The hint is to consider a non-trivial subgroup of minimal order. 2. Relevant equations Lagrange 3. The attempt at a solution Can I use Lagrange to say that there must exist a subgroup H of order pm with m<k? Or even a subgroup H of order p? Although I'm not sure how to justify this. Then if H was cyclic then there must be an element of order p? Again, this is just a guess.