Dear Nikos Apostolakis, Dear Forum,
I am looking for representations of some fp groups in to symmetric
groups. Searching the documentation and the archives I came up with
the following code:
My first question is: Is there a way to specify *a priory* that the
generators will be mapped within a given conjugacy class? For
example I would like all the generators to be mapped to
transpositions. (I work with Wirtinger presentations of knot and
link groups where the generators are in relatively few conjugacy
classes.)
Using slightly different code (the machinery driving `GQuotients'
this would be possible. However this extra testing comes at an extra
cost in runtime. If your image group is (likely to be) Sn, and if
your presentation contains a relator a^2=1 (if the image of a is to
be an involution we can easily demand this, if its not yet in the
presentation) my guess is that `LowIndexSubgroups' actually will run
faster.
The second question has to do with Tietze transformations. The
above process seems to be faster if I first apply the function TzGo
to the presentation. Also checking if the resulting representation
maps in the desired conjugacy cass is easier since there are fewer
generators. However, I need to know the images of the original
generators. So the question is, after I apply TzGo how can I get
the old generators expressed in terms of the new ones? I mean,
by setting "printLevel=2" I can have this information printed out
but how can I use it in a program?
If you use `IsomorphismSimplifiedFpGroup' instead of running the low
level Tietze code, you get a nice homomorphism that gives you all
translation information.
Best,
Alexander Hulpke
-- Colorado State University, Department of Mathematics,
Weber Building, 1874 Campus Delivery, Fort Collins, CO 80523-1874, USA
email: [EMAIL PROTECTED], Phone: ++1-970-4914288
http://www.math.colostate.edu/~hulpke
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