If and are any permutations, then the permutation is called a conjugate of . In group theory, a conjugate operation is very much like a change in coordinate system.

Here's a concrete example from Rubik's Cube. Suppose that you know how to swap two corner pieces that are on the same edge (see Section 9.1; let's call this operation ), but you're faced with a cube where the corners you would like to swap are not on the same edge. No problem--find a simple operation (call it ) that brings the two corners of interest to be on the same edge. If you perform , then , and then ``undo'' (in other words, perform , the net effect will be to move the corners to the same edge, swap the corners on that edge, and then move the corners back to where they began. Doing , then , then is the same as doing --a conjugate of .

Zvezdelina Stankova-Frenkel 2000-10-04