From din5w@server.cs.virginia.edu Fri Oct 20 06:24:11 1995 Received: from virginia.edu (uvaarpa.Virginia.EDU) by life.ai.mit.edu (4.1/AI-4.10) for /com/archive/cube-lovers id AA10327; Fri, 20 Oct 95 06:24:11 EDT Received: from server.cs.virginia.edu by uvaarpa.virginia.edu id aa26937; 19 Oct 95 22:57 EDT Received: from cobra.cs.Virginia.EDU (cobra-fo.cs.Virginia.EDU) by uvacs.cs.virginia.edu (4.1/5.1.UVA) id AA07239; Thu, 19 Oct 95 22:57:16 EDT Posted-Date: Thu, 19 Oct 1995 22:57:15 -0400 (EDT) Return-Path: Received: by cobra.cs.Virginia.EDU (5.x/SMI-2.0) id AA24433; Thu, 19 Oct 1995 22:57:15 -0400 Date: Thu, 19 Oct 1995 22:57:15 -0400 (EDT) From: Dale Newfield X-Sender: din5w@cobra.cs.Virginia.EDU Reply-To: DNewfield@virginia.edu To: cube-lovers@ai.mit.edu Subject: Re: Embedding G in a symmetrical group In-Reply-To: <199510200141.CAA03659@wn1.sci.kun.nl> Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII 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... ...I think I'm just confused--can you alleviate that problem? -Dale Newfield