From mschoene@math.rwth-aachen.de Mon Dec 4 09:10:17 1995 Return-Path: Received: from hurin.math.rwth-aachen.de by life.ai.mit.edu (4.1/AI-4.10) for /com/archive/cube-lovers id AA23100; Mon, 4 Dec 95 09:10:17 EST Received: from samson.math.rwth-aachen.de by hurin.math.rwth-aachen.de with smtp (Smail3.1.28.1 #30) id m0tMZOr-0009KuC.951204.150809; Mon, 4 Dec 95 12:49 MET Received: from hobbes.math.rwth-aachen.de by samson.math.rwth-aachen.de with smtp (Smail3.1.28.1 #11) id m0tMZOr-000I7wC; Mon, 4 Dec 95 12:49 MET Received: by hobbes.math.rwth-aachen.de (Smail3.1.28.1 #26) id m0tMZOq-0009ejC.951204.124936; Mon, 4 Dec 95 12:49 MET Message-Id: Date: Mon, 4 Dec 95 12:49 MET From: Martin Schoenert To: hoey@aic.nrl.navy.mil Cc: Cube-Lovers@life.ai.mit.edu In-Reply-To: hoey@aic.nrl.navy.mil's message of Sun, 3 Dec 95 14:46:30 EST <9512031946.AA24122@sun13.aic.nrl.navy.mil> Subject: Re: Re: Generating Rubik's Cube I have used GAP to compute the subgroup generated by 300 random pairs of elements of G. 151 of those pairs generated the entire group, so the probability is about 50%. I don't think we can figure out the exact number, since we don't know the maximal subgroups of G. One maximal subgroup we know is the derived subgroup (on which the upper bound of 75% is based). Then there are the 8 stabilizers of the corners (of index 8) and the 12 stabilizers of the edges (of index 12). Using those it should be possible to push the upper bound down to something about 60%. Martin. -- .- .-. - .. -. .-.. --- ...- . ... .- -. -. .. -.- .- Martin Sch"onert, Martin.Schoenert@Math.RWTH-Aachen.DE, +49 241 804551 Lehrstuhl D f"ur Mathematik, Templergraben 64, RWTH, 52056 Aachen, Germany