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 (1908–1963)
“Earth has not anything to show more fair:
Dull would he be of soul who could pass by
A sight so touching in its majesty:
This city now doth, like a garment, wear
The beauty of the morning; silent, bare,
Ships, towers, domes, theatres and temples lie
Open unto the fields and to the sky;
All bright and glittering in the smokeless air.”
—William Wordsworth (1770–1850)