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)
“This scene was supposed to be in a saloon, but the censor cut it out. It’ll play just as well.”
—Otis Criblecoblis, U.S. screenwriter. W.C. Fields (W.C. Fields)