> < ^ Date: Tue, 08 Feb 1994 17:10:00 +0100
> < ^ From: Harald Boegeholz <hwb@ix.de >
> < ^ Subject: Re: on permutation group "transversals".
Date:           07 Feb 94 08:53 +0100
From: Paul Igodt  <paul.igodt@kulak.ac.be>

When one looks at the output of
if gp is a well defined permutation group, than one finds a record containing
many "transversals". How should these transversals be understood? E.g. they contain
often many "extra comma's".

These transversals are needed by the algorithm that generates the
stabilizer chain (Schreier/Sims). You have to understand that
algorithm to take any advantage of them, I think.

Is there a procedure in GAP to solve the "word"-problem for permutation groups?
E.g. something like "wordsolve(element, group, group.generators)" ?

I don't think so. I once wrote such a program (by modifying
MakeStabStrong etc. in such a way that it records how new generators
were constructed out of the old generators).

Unfortunately, it was not very useful for "practical" purposes :-):
For Rubik's Cube it produced words with an average length of about
500,000. It also needed quite some memory to compute those. But it
did produce solutions in finite time ;-).

If you are interested in the code (it will probably work better for
smaller groups), I can dig it out and mail it to you.

Harald Boegeholz | hwb@mathematik.uni-stuttgart.de
| os2a@info2.rus.uni-stuttgart.de

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