defined by is a ring homomorphism and thus contains a field hence can be considered as a finite dimensional vector space over
2.) Show that any finite field has order p^n, where p is prime.
I have that Char F = p and the order of a divides p, and I know that the order of a is either 1 or p. I also know that p divides the order of the field, so F must contain an element of order p. I'm just having trouble connecting that to proving any finite field has order p^n.
Any help would be greatly appreciated. Thanks.
let then because