I was asked to prove that given a finite group G, a normal group N in G, and a p-sylow supgroup P in G, then
where is the normalizer of P in G (same with )
I tried to solve it using the homomorphism
I can show that and also that .
all I need now is to show that in order to use the first isomorphism theorem, but for some reason I can manage it.
any help would be appreciated