> < ^ Date: Tue, 08 Feb 1994 16:58:00 +0100
> < ^ From: Steve Linton <sal@dcs.st-and.ac.uk >
> < ^ Subject: Re: on permutation group "transversals".

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 con
often many "extra comma's".

The transversal is realy what is known as a Schreier vector.
The extra commas come from the fact that S.transversal[x] is only
bound if x lies in S.orbit. If so, then

while x <> S.orbit[1] do

will always terminate (and reasonably quickly).

To put it another way, from S.transversal you can compute,
efficiently an element s in S such that S.orbit[1]^s = x, for any x
in S.orbit.

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

Not as far as I know, though it might be possible (I'm guessing) to
do something by defining a homomorphism from a free group to your
permutation group and the looking for a pre-image representative of
the element in question.


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