Group theory describes the rules of operation of sets of numbers or objects, including finite, discrete, topological, and Lie groups. Group theory became one of the central tools in elementary particle physics in the 1960s. Although quantum electrodynamics (QED) operated as the fundamental theory of electricity and magnetism, physicists tried to adapt it to other interactions by making minor changes to it. Quantum electrodynamics (QED) was invariant under transformations that are contained in an Abelian group (i.e., a group on which the defined binary operation is cummutative). Physicists developed a theory similar to QED, except it is invariant under transformations in non-Abelian groups. Eventually, this theory was applied to the strong and weak interactions and incorporated into the standard model of particle physics.

A group is a set of objects, plus an operation that obeys a set of four mathematical rules. The objects may be...