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Thanks to Joachim Neubueser, Frank Celler, and Derek Holt for their

responses regarding my question on infinite matrix groups. I'd like

to make these comments in return:

(1) I think the first method suggested by Derek Holt is very close to what I

had in mind for getting the 'first' 1000 elements of an infinite group;

I will try generating more and more elements of the free group while

watching for repetitions (until I get 1000). As noted there doesn't

seem a GAP function that does that, but I agree that it should be easy

to implement one; an advantage of this is that I know how to add

'selection rules' for which elements to accept. I was hoping to find

something more sophisticated and it seems that such an algorithm exists.

Two catches though! : it is not part of GAP (yet), and it assumes that

you know the defining relations of the group (for this particular problem,

I don't, I only have matrices). This algorithm would be a nice addition

to GAP someday; in the mean time I would be interseted to know more about

the existing software and I think that others might be too. I'll leave it

to Derek's discretion to tell more about his software by e-mail or through

the forum -- when he's not too busy of course :-)

(2) Frank Celler's heuristic method would probably involve the least amount of

work on my part and so I will try it first. I suspect that this would not

really give me the elements that I am looking for but hopefully I'm wrong!

(3) I am glad to get a response from Dr. Neubueser on this since I am well

aware of his work (with others) on the classification of the the four

dimensional space groups; this also makes it easier for me to describe

my "wish-list" as far as crytallographic groups are concerned: the

short (and and I hope not too blunt :-) ) answer is : all the tables

in the book 'Crystallographic Groups in Four Dimensional Space';

It would be so nice to have the generators for all the point groups

as well as the full space groups in dimensions 1 to 4 complemented by

routines to give such standard data as equivalent positions (for

different cernterings) of these groups -- that would make a good part

of the International Tables available at your fingertips.

I realize that the classification was carried out a number of yeares

before GAP was introduced; I am curious to know how much of it can be

recreated within GAP today.

Once again, thanks to all for their help.

Jacob Hirbawi

JcbHrb@CERF.net

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