Cayley's Theorem

A foundational result of abstract group theory showing that every group, however it is defined, can be viewed concretely as a group of permutations. Arthur Cayley stated the correspondence in an 1854 paper but did not explicitly show it was a structure-preserving embedding rather than a mere one-to-one correspondence, so the theorem predates general recognition of its own complete modern proof by decades. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/