fixed field

Let K/F be a field extension with Galois groupMathworldPlanetmath G=Gal(K/F), and let H be a subgroupMathworldPlanetmathPlanetmath of G. The fixed field of H in K is the set

KH:={xKσ(x)=x for all σH}.

The set KH is always a field, and FKHK.

Title fixed field
Canonical name FixedField
Date of creation 2013-03-22 12:08:24
Last modified on 2013-03-22 12:08:24
Owner djao (24)
Last modified by djao (24)
Numerical id 6
Author djao (24)
Entry type Definition
Classification msc 12F10