hi , this result is from text , Abstract Algebra by Dummit and foote . page 120 the result says , if G is a finite group of order n , p is the smallest prime dividing the order of G , then , any subgroup H of G whose index is p is normal and the text gave the proof of this result , but a part of this proof is not obivous for me ! this part is ,all prime divisors (p-1)! are less than p . why is this true ?!! can anyone explain plz ?