A Galois group is a mathematical concept that arises in the field of abstract algebra, specifically in the study of field extensions. It consists of a set of symmetries, or automorphisms, of a field extension that preserve the structure of the field. These symmetries help to understand the solutions of polynomial equations and their relationships. The Galois group is named after the mathematician Évariste Galois, who made significant contributions to the theory of equations. By analyzing the Galois group, mathematicians can determine whether a polynomial can be solved by radicals and explore the connections between different field extensions.