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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 ?

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