[GAP Forum] Rubiks cube and Fp groups

[Alexander Hulpke]

Dear GAP Forum,

On Apr 1, 2006, at 6:49 AM, Rudolf Zlabinger wrote:
> I tested the presentation of a random element of the cubes  
> permutations in a
> finitely presented group.
>

> The Preimage for
> the Free group gave a solution of length 120, the same performed  
> with the Fp
> group, same permutation, resulted in a chain of 84 moves.

>
> The algorithm mentioned in the sample was using stabilizer chains.  
> Is it the
> same for the Fp group I used for my test? Or is there help for a  
> "better"
> algorithm caused by the relators? Or is it pure random behaviour?

The algorithm is the same. I uses random words, thus the different  
length will be due to random behavior. If you construct the same  
homomorphism anew and try you will see some length discrepancies.

>
> By the way, another question to the same sample. There are given "  
> wreath
> products of a 3 cycle (2 cycle) with S(8)". Is it right to  
> interprete them
> as wreath products of the cycles ^ 8 and S(8)?
I suppose you mean ``semidirect'' in the last line. Then yes.

Best wishes,

     Alexander Hulpke