**Symmetries in 20th-century physics**
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Symmetries can be encoded in an algebraic structure known as a group. One of the main properties of groups is their internal composition law: applying two operations in succession produces another operation in the group. This approach has helped to uncover new elementary particles.
In relativity, the Poincaré–Lorentz transformations form a group. In nuclear physics, the strong interaction, which holds the nucleus together, is independent of electric charge. This charge independence is an internal symmetry—namely isospin symmetry relating the neutron and the proton—and is described by the symmetry group SU(2).
Gauge symmetries
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Many transformations take place in ordinary space and are therefore fairly easy to visualize. We can also consider transformations that change a system’s dynamical variables without affecting space and time. The resulting symmetries are called internal symmetries.
