Gauge group (mathematics)

A gauge group is a group of mathematical objects like numbers, shapes and symbols that all follow a certain set of rules. It's like if you had a box with a bunch of different kinds of toys in it. Each toy has its own way it should be used, and you wouldn't mix up the Lego bricks with the dolls. That's how a gauge group works. All the elements of the group have something in common, like how the toys share the same box, and each element has its own special rule that it must follow.