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 .
|Date of creation||2013-03-22 15:56:21|
|Last modified on||2013-03-22 15:56:21|
|Last modified by||Wkbj79 (1863)|