Computing whether a particular finitely presented group is infinite with GAP

Question

I am working with GAP 4 and trying to check whether a finitely presented group is infinite. Since the Size-function dies on me I followed the suggestion in the GAP manual to try working with the low index subgroups. Based on https://www.gap-system.org/Doc/Examples/cavicchioli.html I came up with the following code:

F:=FreeGroup(["f1", "f2", "t1", "t2", "t3"]);
AssignGeneratorVariables(F);
T:=F/[f1^2,f2^2,t1^3,t3^3,(t2)^5,(t1*f1)^2,t3^-1*f1*t2,f2*t2^-1*t1^-1];

maxIndex:=30;
u := LowIndexSubgroupsFpGroup(T,TrivialSubgroup(T),maxIndex);
u := Filtered(u,i->Index(T,i)>1);
Collected(List(u,i->IsInfiniteAbelianizationGroup(i)));

Which gives me the result: [ [ true, 1 ], [ false, 30 ] ]

Can this be counted as a proof that the finitely presented group above is infinite?

This question is related to Finding low-index normal subgroups of finitely presented groups in GAP.

Answer 1

Yes, I believe so.

If the abelianisation $G^{{\rm ab}}$ of a group $G$ is infinite, so is $G$. If a subgroup $G$ of a group $H$ is infinite, so is $H$.

I don't see any obvious mistakes in your programme.