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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