Frobenius map

Let K be any field of characteristicPlanetmathPlanetmath p>0, and suppose K contains the finite fieldMathworldPlanetmath 𝔽q of size q, where q=pr. The qth power Frobenius mapPlanetmathPlanetmath on K is the map Frobq:KK defined by Frobq(x):=xq.

If K is perfectPlanetmathPlanetmath, then Frobq is an automorphismPlanetmathPlanetmathPlanetmath of K which fixes 𝔽q, and accordingly is a member of the Galois groupMathworldPlanetmath Gal(K/𝔽q).

Title Frobenius map
Canonical name FrobeniusMap
Date of creation 2013-03-22 12:34:52
Last modified on 2013-03-22 12:34:52
Owner djao (24)
Last modified by djao (24)
Numerical id 6
Author djao (24)
Entry type Definition
Classification msc 12E20
Classification msc 11T99
Related topic FrobeniusAutomorphism