   Date: Tue, 28 Dec 93 00:43:02 +0100   From: Dik T. Winter <Dik.Winter@cwi.nl >
~~~  Subject: Re: Group theory basics (Re: Symmetry)

>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.

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...     