I am having some difficulties here and would like some guidance.

Let be a group such that where are primes and and is not a divisor of . Show that is abelian.

What I can determine so far is that has p-sylow group of order and a q-sylow group of order and that both must be abelian.

Additionally I can try to eliminate the possibilities for (the number of p,q-sylow groups).

What I got is that the options for are and for they are . but I can't get anywhere from here.

Any help appreciated.