biquadratic extension
A biquadratic extension of a field is a Galois extension of such that is isomorphic to the Klein 4-group. It receives its name from the fact that any such is the compositum of two distinct quadratic extensions of . The name can be somewhat misleading, however, since biquadratic extensions of have exactly three distinct subfields that are quadratic extensions of . This is easily seen to be true by the fact that the Klein 4-group has exactly three distinct subgroups of order (http://planetmath.org/OrderGroup) 2.
Note that, if , then is a biquadratic extension of if and only if none of , , and are squares in .
Title | biquadratic extension |
---|---|
Canonical name | BiquadraticExtension |
Date of creation | 2013-03-22 15:56:21 |
Last modified on | 2013-03-22 15:56:21 |
Owner | Wkbj79 (1863) |
Last modified by | Wkbj79 (1863) |
Numerical id | 7 |
Author | Wkbj79 (1863) |
Entry type | Definition |
Classification | msc 11R16 |
Related topic | BiquadraticField |
Related topic | BiquadraticEquation2 |