From mschoene@math.rwth-aachen.de Sat Dec 10 09:21:41 1994 Return-Path: Received: from samson.math.rwth-aachen.de by life.ai.mit.edu (4.1/AI-4.10) for /com/archive/cube-lovers id AA09060; Sat, 10 Dec 94 09:21:41 EST Received: from hobbes.math.rwth-aachen.de by samson.math.rwth-aachen.de with smtp (Smail3.1.28.1 #11) id m0rGSde-000MPHC; Sat, 10 Dec 94 15:19 MET Received: by hobbes.math.rwth-aachen.de (Smail3.1.28.1 #19) id m0rGSdd-0000PvC; Sat, 10 Dec 94 15:19 PST Message-Id: Date: Sat, 10 Dec 94 15:19 PST From: "Martin Schoenert" To: cube-lovers@life.ai.mit.edu In-Reply-To: "Jerry Bryan"'s message of Thu, 8 Dec 1994 15:02:33 -0500 (EST) <9412082002.AA14755@life.ai.mit.edu> Subject: Re: Re: Models for the Cube I wrote in my e-mail message of 1994/12/07 But C is not the largest such group. The largest such group is M, i.e., the full group of symmetries of the entire cube. This is the reason why I prefer to view G as a subgroup of MG, which is the semidirekt product of M and G, even though I realize that MG is not physically realizable. Jerry Bryan answered in his e-mail message of 1994/12/07 But can't you speak of conjugates such as m'gm without regard to G being a subgroup of MG? I agree that MG seems like a very useful group, and it is a very nice model of what is going on. But doesn't g in G imply m'gm in G whether I ever heard of MG or not? Yes I certainly could. I think it is only a matter of taste. You seem to favor the physical model. There the reflection has no real realization, and it makes sense to distinguish between the rotations and the reflection. I look at the problem more from the computational aspect. I view the whole thing as a permutation group, and then there is no real reason to distinguish between the rotations and the reflection (both being ordinary permutations on 54 points). And when working with those groups in GAP, it is certainly a lot more convenient to work in MG and treat all of M uniformly, then to work in CG and to handle the reflection specially. Have a nice day. Martin. -- .- .-. - .. -. .-.. --- ...- . ... .- -. -. .. -.- .- Martin Sch"onert, Martin.Schoenert@Math.RWTH-Aachen.DE, +49 241 804551 Lehrstuhl D f"ur Mathematik, Templergraben 64, RWTH, 52056 Aachen, Germany