[GAP Forum] Presentation and computations

[Horn, Max, Prof. Dr.]

Dear lopo apelo kosho,

> On 31. Mar 2020, at 15:40, lopo apelo kosho <helo_07 at yahoo.com> wrote:
> 
> Dear friends; 
> I was wondering if you could advice with the following:
> I have called the group F= [36,6] throuw presention by generators and relations. 
> Now I am forming groups (say, H...) generated by some generators of F.  
> The problem is that: 
> GAP did not recognize H as subgroup of G.
> 
> I do not know how to handle this situation. 
> 
> I am attaching a sample part of the GAP session: 
> 
> gap> f:=FreeGroup(3);
> <free group on the generators [ f1, f2, f3 ]>
> gap> a:=f.1;b:=f.2;c:=f.3;
> f1
> f2
> f3
> gap> F:=f/[a^3,b^4,c^3,a^b*a,c^a*c^2,c^b*c^2];
> <fp group on the generators [ f1, f2, f3 ]>
> gap> h:=Group(a*c);
> Group([ f1*f3 ])

Note that you defined a and c above as elements of the free group f, NOT as elements of its quotient F.

To fix this, redefine a,b,c as elements of F, either similar to how you defined them above, or like this:

  AssignGeneratorVariables(F)

Then define h in terms of these new generators, and all should work.

Best regards
Max


> gap> IsSubgroup(F,h);
> false
> gap> Order(h);
> infinity
> gap>
> 
> 
> I WOULD BE MOOR THAN GRATEFUL FOR ANY HELP.
> Thank you
> 
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-- 
Prof. Dr. Max Horn
University of Siegen
Department of Mathematics
Emmy Noether Campus
Walter-Flex-Straße 3
57072 Siegen
Tel. (+49) 271 740-2868
E-Mail: max.horn at uni-siegen.de