Re: Complexes of a Group?

Hatto von Aquitanien wrote:

"(2) A complex, K, is a collection of group elements,
K = (K1, K2, ...,Kn) where the ordering in the list
is not important.A complex can be multiplied by a
single group element (say, X) or by another complex
(say, R).For example, K X = (K1X, K2X, ..., KnX)
and KR = (K1R1, K1R1, ..., K1Rm, K2R1, ..., KnRm)
These multiplications are defined such that elements
that result from them are included in the product
only once, regardless of how often they are generated."


The term complex is not indexed in Fraleigh except
in connection with Gaussian numbers, and I am not
getting a lot of hits on the Internet when I search
on filters such as `Complexes of a Group coset'.
Is this a common use of the term 'complex' in
contemporary mathematics? Does the concept
'complex' go by a different name?

I guess I'm in the mood for ranting about this kind
of writing now.

The term "complex" seems to me nothing more than
what "set" refers to, and I have no idea why someone
would try to make things more difficult by creating
non-standard terminology, especially when it's
explained in such a complicated sounding way.

Also, I assume we're dealing with finite groups,
or at least we're restricting ourselves to finite
collections of group elements from a possibly
infinite group. Even in chemistry I see no reason
why one would want to restrict themselves in this way.

The excerpt reads like someone saying the following,
in a non-physics book that is trying to explain some
of the fundamental principles of classical mechanics:

"The power, or energy (i.e. force), in a non-stationary
material object increases geometrically with its motion.
The physico-algebraic identities for the motion's energy
can be solved to find the roots of an object's flight
path in accordance with Newton's three laws of activity . . ."

(Exercise for sci.math -- See if you can identify over
20 problems, in content or in style, with the wording
of these last two sentences.)

For example:

"These multiplications are defined such that elements ..."

The multiplications (Is this supposed to name the outputs
or name the process? I can't even tell.) are already defined,
if we have a group. What's being defined here are not the
multiplications, but rather a particular collection
of outputs of the multiplications.

"... the ordering in the list is not important"

I can see how someone very new to abstract math
could get very confused at this point.

"... elements that result from them are included in
the product only once ..."

Which, of course, leaves open the question of whether
elements *not obtained* in this manner can also belong
to the complex.

Dave L. Renfro

.