Frobenius For Finite Fields
Let Fq be the finite field of q elements, where q=pe. F fixes Fp by the argument above. If e=2, then F2, the second iterate of Frobenius, fixes p2 elements, so it will fix Fp2. In general, Fe fixes Fpe. Furthermore, F will generate the Galois group of any extension of finite fields.
Read more about this topic: Frobenius Endomorphism
Famous quotes containing the words finite and/or fields:
“For it is only the finite that has wrought and suffered; the infinite lies stretched in smiling repose.”
—Ralph Waldo Emerson (1803–1882)
“Smart lad, to slip betimes away
From fields where glory does not stay,
And early though the laurel grows
It withers quicker than the rose.”
—A.E. (Alfred Edward)