From BRYAN@wvnvm.wvnet.edu Fri Oct 13 16:40:29 1995 Return-Path: Received: from WVNVM.WVNET.EDU by life.ai.mit.edu (4.1/AI-4.10) for /com/archive/cube-lovers id AA12120; Fri, 13 Oct 95 16:40:29 EDT Received: from WVNVM.WVNET.EDU by WVNVM.WVNET.EDU (IBM VM SMTP V2R3) with BSMTP id 4011; Fri, 13 Oct 95 15:01:31 EDT Received: from WVNVM.WVNET.EDU (NJE origin BRYAN@WVNVM) by WVNVM.WVNET.EDU (LMail V1.2a/1.8a) with BSMTP id 2466; Fri, 13 Oct 1995 15:01:32 -0400 Message-Id: Date: Fri, 13 Oct 1995 15:01:31 -0400 (EDT) From: "Jerry Bryan" To: "Dan Hoey" , Subject: Re: Using 5 Generators In-Reply-To: Message of 10/11/95 at 22:56:15 from hoey@aic.nrl.navy.mil On 10/11/95 at 22:56:15 hoey@aic.nrl.navy.mil said: >[in Q2] >> The four rotations are i, b, bb, and bbb, where we use lower case >> letters to simulate Frey and Singmaster's script notation for rotations. >> For example, b is the whole cube rotation consisting of grasping >> the Back face and rotating the whole cube (not just the Back face) >> clockwise by 90 degrees. >The reflections are similarly rrv, rrbv, ttv, and ttbv, where t and r >are the whole-cube rotations by the Top and Right faces, and v is the >central inversion. I am not quite sure why it took me so long to figure out that Q2-conjugation was the appropriate symmetry when generating G without B and B'. With the wisdom if hindsight, it is perhaps because the Q2 subgroup of M could be described as fixing the B and F face centers, and I was thinking only in terms of fixing the B face center. Obviously, you cannot fix the B face center without also fixing the F face center. Thus, it is clear that Q2-conjugation is also the appropriate symmetry when generating G without F and F'. Q1 and Q3 are subgroups of M which are conjugate with Q2 in Dan's taxonomy of subgroups of M. Q1 fixes the T and D face centers, and would be the appropriate symmetry when generating G without T and T', or without D and D'. Q3 fixes the R and L face centers, and would be the appropriate symmetry when generating G without R and R', or without L and L'. = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = 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