What is a group structure?

Hi everyone,

I am currently doing a project on the Rubik's Cube and was trying to find a clear explanation online as to what the cube group's structure was, however, I soon realised I wasn't really sure what a group structure was :S can anyone shed some light on this for me?

Cheers

Re: What is a group structure?

Ah ok I see now. If considering the 2x2 Rubik's cube would it be correct to say that:

R = A_8 |X (Z/3Z)^8

Where R is Rubik's Group and A_8 is the 8th alternating group?

Cheers.

Re: What is a group structure?

Quote:

Originally Posted by

**Deveno** the "group structure" arises because every sequence of moves is reversible (so we have inverses), and subsequent consecutive moves can be regarded as compositions of "basic moves" (turning one face 90 degrees), which assures us of associativity (U then F then R is the same as (F then R) preceded by U). the identity is "the empty move" (doing nothing).

Another way of seeing that you have a group acting on a set is that when you do a move you are doing no less than permuting the cubies! Permutations=groups, QED...

A nice corollary of the group structure is that if you start with a solved cube, fix a move and apply it repeatedly to your cube then you will end up with the solved cube again. This is, as the kids say, `cool'.

Re: What is a group structure?

that only happens with "finite" cubes

Re: What is a group structure?

Quote:

Originally Posted by

**Deveno** that only happens with "finite" cubes

Yes.