From mschoene@math.rwth-aachen.de Wed Dec 7 16:30:24 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 AA05937; Wed, 7 Dec 94 16:30:24 EST Received: from hobbes.math.rwth-aachen.de by samson.math.rwth-aachen.de with smtp (Smail3.1.28.1 #11) id m0rFSGg-000MPPC; Wed, 7 Dec 94 20:43 MET Received: by hobbes.math.rwth-aachen.de (Smail3.1.28.1 #19) id m0rFSGg-0000PsC; Wed, 7 Dec 94 20:43 PST Message-Id: Date: Wed, 7 Dec 94 20:43 PST From: "Martin Schoenert" To: cube-lovers@life.ai.mit.edu Subject: Corrections Dan Hoey writes in his e-mail message of 1994/11/08 Martin.Schoenert@math.rwth-aachen.de writes: The way I view this is as follows. The entire cube group C is a permutation group group on 6*9 points, generated by the six face turns U, D, L, R, F, B; the three middle slice turns M_U, M_L, M_F; and the reflection S. This group has a subgroup M of symmetries of the cube (of order 48), generated by U M_U D', L M_L R', F M_F B', and S. Another subgroup is G, generated by the six face turns, which has index 48 in G. G is a normal ^ divisor of C, G is the semidirect product of M and G. The same is ^ true for GE and GC. I think two of those G's are supposed to be C's, right? Correct (wouldn't make any sense for a group G to be a subgroup in itself of index 48 ;-). Dan Hoey continues As for when I wrote M class Edge Corner Corner times edge (class size) F.P. F.P. / (96*class size) ^^^^^^^^^^^^^^^^^^^^^^ That's not a typo. I was just saying that column 4 is equal to column 2 times column 3, divided by column 1, divided by 96. Perhaps I should have factored column 1 out of columns 2 and 3 first to avoid this confusion. Again you are correct. But it was confusing, at least to me. 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