This term associates to every field, a corresponding group property. In other words, given a field, every group either has the property with respect to that field or does not have the property with respect to that field
This term is related to: Galois theory
View other terms related to Galois theory | View facts related to Galois theory
Definition with symbols
If no field is specified, we assume that the field is , the field of rational numbers.
The inverse Galois problem essentially asks for which finite groups can be expressed as the Galois group of a field extension of .
Definition in terms of the universal Galois group
A group is Galois-realizable over a field if it is the quotient of the universal Galois group of by a normal subgroup which is closed under the naturally given Krull topology.
Relation with other properties
The following properties are known to be weaker than the property of being Galois-realizable over :