Rubik Cube finite non-abelian group

Question

I was reading the following paper from MIT: http://web.mit.edu/sp.268/www/rubik.pdf

The paper is not difficult to understand, it is more or less a short introduction into group theory, taking the Rubik's Cube as an example of a finite, non-abelian group.

My question: How can I use this fact to find possible ways for solving the cube, if you know what I mean? There are several ways for solving the cube, which seem to me more intuitive rather than a direct result of the group properties.

So if somebody would ask you "It is nice that Rubik's Cube can be seen as an example of a finite group, but what can I do with this knowledge? ", what would you answer?

Answer 1

From a theoretical perspective, solving Rubik's cube is a nice example of the Schreier-Sims algorithm in action, although applying the algorithm will not give in general the quickest solution.

Answer 2

The book by Alexander Frey and David Singmaster, Handbook of Cubik Math, solves the cube using such group-theoretic concepts as cycles, equivalences, identities, inverses, order, commutativity, and conjugates.

There's also a book by David Joyner, Adventures in Group Theory, which has a lot of stuff about the Rubik cube, but I don't know whether it does what you want.