The question is:
There's a group G, with order pm, where p is a prime number and mcd(p,m) = 1. We suppose that G has an unique p-Sylow subgroup P. Proof that P is a normal subgroup of G.
How I understand Sylow's First Theorem, this is obvious from the definition? I've always struggled with giving formal proves, maybe someone can help me in this case, thanks!