From dik@cwi.nl  Mon Dec 27 18:43:04 1993
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Date: Tue, 28 Dec 93 00:43:02 +0100
From: Dik.Winter@cwi.nl
Message-Id: <9312272343.AA25571.dik@boring.cwi.nl>
To: Cube-Lovers@life.ai.mit.edu
Subject: Re:  Group theory basics (Re: Symmetry)

One additional remark:

 > > Well, if P is a rotation operator, you could perform a rotation
 > > two ways.  I guess one is pre-multiplication and one is
 > > post-multiplication.

 > >     1)  For i = 1 to 24  B(i) = A(P(i))

 > I would write this as B = P A, and say that A is premultiplied by P,
 > or equivalently that P is postmultiplied by A.

There is quite a bit of confusion about this.  When permutation
groups are considered; even text-books do not agree.  When A and P
are permutations you can find both that P A means: apply P first, A next,
but also: apply A first, P next.  (The first meaning comes from the pure
group theorists, the second meaning more from the algebra inclined.)

Sorry to confuse the issue, but when I read such texts I have always to
think hard to get at the intended meaning.  I think the functional
notation is much clearer and leads to less confusion.

Of course, doing notations for cube rotations the group theorists
notation is applied, but when doing abstract operations...