[GAP Forum] Re: Tietze

[Alexander Hulpke]

Dear GAP-Forum,

Michael Hartley wrote:

> I've looked through the functions relating to relations and Tietze
> Transformations. However, I can't find anything that will take a
> presentation object and give GAP the actual relators within it
> (TzPrintRelators() gives *me* the relators, but not GAP). I have a large
> list of permutation groups, and I want to do the following for each group
> (actually, each generating set) in the list :

> grp := Group(gens);
> pres := PresentationViaCosetTable(grp);
> rels := GetRelatorsSomehow(pres);   <-- need help here
> if (MyTest(rels)) then
>    Print("the group generated by ",gens," passes my test \n");
> fi;
> 
> Any advice? Does the function I want actually exist? Specifically, I want
> to check that there doesn't exist a relator using all the generators of the
> group.

You could use:
grp2:=FpGroupPresentation(pres);
rels:=RelatorsOfFpGroup(grp2);

Note that the free generators are
FreeGeneratorsOfGroup(grp2);

Alternatively, you could use 
hom:=IsomorphismFpGroupByGenerators(grp,gens);
grp2:=Image(grp);
which does a slightly different kind of rewriting in one call.

I hope this is of help,

  Alexander Hulpke

PS: Given that the Forum email goes to hundreds of people I would suggest
that when replying to a ``digest'' mail to delete the irrelevant contents of
the digest as well as changing the subject line.

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