I refer to http://www.gap-system.org/Doc/Examples/rubik.html as given by Martin Schönert.
I tested the presentation of a random element of the cubes permutations in a finitely presented group. I took the free group in the sample and formed a Fp group giving the relators f ^ 4 for all generators of the free group, as this is also given by the original generators. Of course, its a infinite group again, as unnecessarily also tested by the Newman Infinity Criterion. 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. To be secure I tested the image also in reverse order successfully, as given by the sample. The random permutation was in both cases (1,22,33,17,19,40,30,35,16,3,6,25,46,24,9,41,27,11,8,14,43)(2,13,31,29,15,42 , 28)(4,5,39,18,37)(7,12,10,26,47)(20,45,36,44,23,21,34)(32,38,48) . 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? 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)? best regards, Rudolf Zlabinger
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