[GAP Forum] Simplified Fp Group

Robert Morse rm43 at evansville.edu
Wed Oct 29 03:06:09 GMT 2008

Dear Josh,

The commands you are looking for are


The first does the Tietze transformations and returns the simplified
Fp group and the second gives an isomorphism from the original group
to the simplified one.


gap> G := Image(IsomorphismFpGroup(DihedralGroup(8)));
<fp group of size 8 on the generators [ F1, F2, F3 ]>
gap> SimplifiedFpGroup(G);
<fp group on the generators [ F1, F2 ]>
gap> IsomorphismSimplifiedFpGroup(G);
[ F1, F2, F3 ] -> [ F1, F2, F2^-2 ]

Hope this helps.

Regards, Robert F. Morse

On Tue, Oct 28, 2008 at 9:44 PM, Josh Roberts <jrobts at gmail.com> wrote:
> Suppose I give a finitely presented group F/R, where
> F:=FreeGroup("a","b",etc) and R is a list of words in "a", "b", etc.  I then
> use TzGoGo to simplify the presentation. I can do G:=FpGroupPresentation to
> get the new presentation. But how can I obtain the generators and relators
> again? If I do f:=GeneratorsofGroup(G) for a list of the generators and
> r:=RelatorsOfFpGroup(G) for a list of the relators f/r gives an error.
> I understand that this is caused by f being a list and not actually a free
> group. But is there a way to build the group using the new, simplifed
> presentation? I want to be able to use f/r and get my group.
> Thanks,
> Josh
> --
> Josh Roberts, Graduate Student
> University of Kentucky - Mathematics
> http://www.ms.uky.edu/~jroberts
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