From BRYAN@wvnvm.wvnet.edu Fri Oct 20 11:18:11 1995 Return-Path: Received: from WVNVM.WVNET.EDU by life.ai.mit.edu (4.1/AI-4.10) for /com/archive/cube-lovers id AA22251; Fri, 20 Oct 95 11:18:11 EDT Received: from WVNVM.WVNET.EDU by WVNVM.WVNET.EDU (IBM VM SMTP V2R3) with BSMTP id 6897; Fri, 20 Oct 95 09:37:34 EDT Received: from WVNVM.WVNET.EDU (NJE origin BRYAN@WVNVM) by WVNVM.WVNET.EDU (LMail V1.2a/1.8a) with BSMTP id 7044; Fri, 20 Oct 1995 09:37:34 -0400 Message-Id: Date: Fri, 20 Oct 1995 09:37:33 -0400 (EDT) From: "Jerry Bryan" To: "Cube Lovers List" Subject: Re: Embedding G in a symmetrical group In-Reply-To: Message of 10/19/95 at 22:57:15 from din5w@virginia.edu On 10/19/95 at 22:57:15 Dale Newfield said: >On Fri, 20 Oct 1995, Michiel Boland wrote: >> It is clear that the group G of the cube (the one with >> 4.3252x10^19 elements) can be embedded in a symmetrical group, e.g. >> S_48, since each move of the cube can be seen as a permutation of 48 >> objects. >Um...If I were a better net.person, I'd look up which version of the cube >has that number of elements, but wouldn't it be correct to say that each >move of the cube is a permutation of the pieces of the cube, i.e. the 26 >cubies? (Or even, depending on which cube-model you are using(This is >what I should have looked up), if you ignore center cubie orientation, >the 20 cubies?) >If that logic holds, then the largest possible S_n would be S_20, much >less than the 32 that you claim is minimal... You are forgetting the twists of the corner cubies and the flips of the edge cubies. As an aside, the S_48 upper bound is already based on ignoring the face centers (i.e., 8 facelets on each of 6 faces of the cube). = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = Robert G. Bryan (Jerry Bryan) (304) 293-5192 Associate Director, WVNET (304) 293-5540 fax 837 Chestnut Ridge Road BRYAN@WVNVM Morgantown, WV 26505 BRYAN@WVNVM.WVNET.EDU