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:
“All finite things reveal infinitude:”
—Theodore Roethke (19081963)
“Ah happy hills! ah pleasing shade!
Ah fields beloved in vain!
Where once my careless childhood strayd,”
—Thomas Gray (17161771)