Compact groups

Compact groups are mathematical structures in the field of group theory, which is a branch of abstract algebra. They consist of a set of elements along with an operation that combines them, satisfying specific rules. The term "compact" refers to a property that ensures these groups are closed and bounded, meaning they don't stretch infinitely and can be contained within a finite space. Compact groups are significant in various areas of mathematics and physics, as they often simplify complex problems and help to describe symmetrical structures in nature and theories. Examples include rotations in three-dimensional space.