[GAP Forum] Using GAP to generate group by relations

[Jay Taylor]

Dear Linda,

What you want to do is create a finitely presented group, for which the
documentation is given here

http://www.gap-system.org/Manuals/doc/htm/ref/CHAP045.htm

What you first need to do in GAP is create a free group then quotient
out by the appropriate relations. For instance the following should
achieve the group that you want in GAP

gap> F:= FreeGroup( "a", "b" );;
gap> a:=F.1;; b:=F.2;;
gap> G:= F / [ a^4, b^4, (a*b)^2, (a^3*b)^2 ];

The first line generates a free group with two generators "a" and "b".
The next line creates variables "a" and "b" and assign the generators of
F to them. The "a" and "b" in the first line are merely place holder
names, not variables that can be interacted with in GAP. The final line
then creates the group G by quotienting out by the appropriate relations.

I hope this helps.

-Jay

Linda Cupples wrote:
> Hey,
> 
> I've been having trouble with mathematica and this group I'm working with,
> the abstractalgebra function "GenerateGroupByRelations[]" wasn't liking the
> group so I've started reading through the documentation for GAP.
> 
> For the record the mathematica command I was using was
> 
> G = GenerateGroupoidByRelations[{a, b}, {a^4 == e, b^4 == e, a ** b ** a **
> b == e, a^3 ** b ** a^3 ** b == e}, SizeLimit -> 60]
> 
> I haven't been able to find a similar function like this to generate a
> group by relations, like a^4 = e and so on,
> 
> Is it possible to do this using GAP?
> 
> Thanks in advance,
> 
> Linda
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-- 
Jay Taylor
http://www.abdn.ac.uk/~r01jmt8/