We'd like to use analytics cookies to understand which symbols people look up, so we know what to research next. They are not used for advertising and we set none of them unless you say yes. What we store.
Gal with a field extension in brackets, the symmetries of a polynomial's roots.
Also known as: Galois group, Gal, Automorphism group of an extension
The Galois group of an extension is the set of ways to shuffle the new elements without disturbing the old ones. Its structure decides whether a polynomial can be solved by radicals, which is what makes it the bridge between group theory and equation solving.
Denotes the group of field automorphisms of an extension that fix the base field pointwise.
Contexts: Mathematics
Determines solvability by radicals: a polynomial is solvable exactly when its Galois group is a solvable group.
Contexts: Mathematics
The three letters G, a and l followed by a bracketed pair of capital letters separated by a slash.