Resolvent (Galois theory)
CONCEPT IN GALOIS THEORY
Lagrange resolvents; Lagrange resolvent; Lagrange Resolvent; Resolvent quadratic
In Galois theory, a discipline within the field of abstract algebra, a resolvent for a permutation group G is a polynomial whose coefficients depend polynomially on the coefficients of a given polynomial p and has, roughly speaking, a rational root if and only if the Galois group of p is included in G. More exactly, if the Galois group is included in G, then the resolvent has a rational root, and the converse is true if the rational root is a simple root.