area of abstract algebra known as Galois theory, the Galois group of a certain type of field extension is a specific group associated with the field extension...

In mathematics, Galois theory, originally introduced by Évariste Galois, provides a connection between field theory and group theory. This connection...

release from prison, Galois fought in a duel and died of the wounds he suffered. Galois was born on 25 October 1811 to Nicolas-Gabriel Galois and Adélaïde-Marie...

absolute Galois group GK of a field K is the Galois group of Ksep over K, where Ksep is a separable closure of K. Alternatively it is the group of all automorphisms...

development of Galois theory. In its most basic form, the theorem asserts that given a field extension E/F that is finite and Galois, there is a one-to-one...

and roots similar to the formula above. Modern Galois theory generalizes the above type of Galois groups by shifting to field theory and considering field...

automorphism group Aut(E/F) is precisely the base field F. The significance of being a Galois extension is that the extension has a Galois group and obeys...

In mathematics, a Galois module is a G-module, with G being the Galois group of some extension of fields. The term Galois representation is frequently...

In mathematics, a finite field or Galois field (so-named in honor of Évariste Galois) is a field that contains a finite number of elements. As with any...

is a finite field extension of F whose Galois group is G. All subgroups and quotient groups of cyclic groups are cyclic. Specifically, all subgroups...