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:
“Are not all finite beings better pleased with motions relative than absolute?”
—Henry David Thoreau (1817–1862)
“The landscape was clothed in a mild and quiet light, in which the woods and fences checkered and partitioned it with new regularity, and rough and uneven fields stretched away with lawn-like smoothness to the horizon, and the clouds, finely distinct and picturesque, seemed a fit drapery to hang over fairyland. The world seemed decked for some holiday or prouder pageantry ... like a green lane into a country maze, at the season when fruit-trees are in blossom.”
—Henry David Thoreau (1817–1862)