Galois Group

In Galois theory, a branch of abstract algebra, the Galois group of a field extension is a symmetry group that characterizes how the extension relates to its base field, with each element of the group a transformation of the extension that leaves every element of the base field fixed. The fundamental theorem of Galois theory connects fields and groups in this way, letting group-theoretic tools be brought to bear on problems in field theory, such as describing the solutions of quintic polynomials; the whole subject of studying field extensions through their Galois groups is named Galois theory, in honor of Evariste Galois, who first discovered them. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/