From BRYAN@wvnvm.wvnet.edu Mon Jan 2 23:07:26 1995 Return-Path: Received: from WVNVM.WVNET.EDU by life.ai.mit.edu (4.1/AI-4.10) for /com/archive/cube-lovers id AA25455; Mon, 2 Jan 95 23:07:26 EST Message-Id: <9501030407.AA25455@life.ai.mit.edu> Received: from WVNVM.WVNET.EDU by WVNVM.WVNET.EDU (IBM VM SMTP V2R2) with BSMTP id 5142; Mon, 02 Jan 95 23:00:17 EST Received: from WVNVM.WVNET.EDU (NJE origin BRYAN@WVNVM) by WVNVM.WVNET.EDU (LMail V1.2a/1.8a) with BSMTP id 3296; Mon, 2 Jan 1995 23:00:17 -0500 X-Acknowledge-To: Date: Mon, 2 Jan 1995 23:00:01 EST From: "Jerry Bryan" To: "Cube Lovers List" Subject: Re: Normal Subgroups of G In-Reply-To: Message of 12/30/94 at 15:17:00 from , Martin.Schoenert@math.rwth-aachen.de On 12/30/94 at 15:17:00 Martin Schoenert said: >Basically the same argument works for GE. But there is one exception. >Namely VE has one normal subgroup of size 2 , generated by the element >(1,1,...,1;). You may not recognize this element, but it is >in fact the superflip, which flips all twelve edges. I shall call this >subgroup Z. >Thus GE has 5 normal subgroups GE, GE', VE, Z, and <1>. I am still absorbing this article, which exceeds my current knowledge of group theory. But at the risk of asking a dumb question, doesn't the center of GE (and of G) in fact consist of more than just the Superflip and the identity? Does it not also include the Pons Asinorum and the composition of the Pons Asinorum and the Superflip? Call the Pons Asinorum P and the Superflip E. I think you are saying Z={I,E}. But isn't the center {I,P,E,PE}, with subgroups {I,P}, {I,E}, {I,PE}, and {I}? These should all be central, and hence also normal, I would think. = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = 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