Cayley's theorem

Cayley's theorem states that any group—a mathematical structure made up of elements combined by a specific operation—can be represented as a group of permutations, which are rearrangements of a set. Essentially, it means that every group can be viewed as acting on some set by shuffling its elements without changing the group's structure. This helps us understand complex groups by analyzing how they permute objects, providing a universal way to see all groups as arrangements or symmetries within a larger set.