[GAP Forum] Basic question, order of fpgroup

[Vipul Naik]

If you put commutation relations between the pairs that are separated
by more than 1, it should work. Add the relations Comm(f.1,f.3),
Comm(f.2,f.4), and Comm(f.1,f.4). You can remove all the fourth power
relations.

Here's the code:

f := FreeGroup(4);;
G := f/[f.1^2,f.2^2,f.3^2,f.4^2,(f.1*f.2)^3,(f.2*f.3)^3,(f.3*f.4)^3,Comm(f.1,f.3),Comm(f.2,f.4),Comm(f.1,f.4)];

Vipul

* Quoting KCHM who at 2011-07-27 16:27:39+0000 (Wed) wrote
> I have used GAP in a small way off and on for several years but still regard 
> myself as a novice. I am having trouble with the code below and wonder if I 
> am just making some elementary mistake. If some experienced person could 
> glance at it for me, I'll be very grateful. 
> 
> >>>>>>>>>>>>>
> 
> f:=FreeGroup(4);;
> G:=f/[f.1^2,f.2^2,f.3^2,f.4^2,
> (f.1*f.2)^3,(f.1*f.3)^3,(f.1*f.4)^3,(f.2*f.3)^3,(f.2*f.4)^3,(f.3*f.4)^3,
> (f.1*f.2*f.1*f.3)^4,(f.1*f.2*f.1*f.4)^4,
> (f.1*f.3*f.1*f.4)^4,(f.1*f.3*f.1*f.2)^4,
> (f.1*f.4*f.1*f.2)^4,(f.1*f.4*f.1*f.3)^4,
> (f.2*f.3*f.2*f.4)^4,(f.2*f.3*f.2*f.1)^4,
> (f.2*f.4*f.2*f.1)^4,(f.2*f.4*f.2*f.3)^4,
> (f.2*f.1*f.2*f.3)^4,(f.2*f.1*f.2*f.4)^4,
> (f.3*f.4*f.3*f.2)^4,(f.3*f.4*f.3*f.1)^4,
> (f.3*f.1*f.3*f.2)^4,(f.3*f.1*f.3*f.4)^4,
> (f.3*f.2*f.3*f.1)^4,(f.3*f.2*f.3*f.4)^4,
> (f.4*f.1*f.4*f.2)^4,(f.4*f.1*f.4*f.3)^4,
> (f.4*f.2*f.4*f.1)^4,(f.4*f.2*f.4*f.3)^4,
> (f.4*f.3*f.4*f.2)^4,(f.4*f.3*f.4*f.1)^4];
> 
> <<<<<<<<<<<
> 
> (If the fourth powers were squares, this would be the symmetric group S_5.
> I have tried with just a minimal set of relations.)
> 
> To start I want the order of G. With `Size(G);' `Order(G);' `IsFinite(G);'
> I just get several (8 or 9) iterations of
> 
> #I  Coset table calculation failed -- trying with bigger table limit
> 
> and then 
> 
> exceeded the permitted memory (`-o' command line option) at
> prev[2 * limit] := 2 * limit - 1;
>  called from
> TCENUM.CosetTableFromGensAndRels( fgens, grels, fsgens ) called from
> CosetTableFromGensAndRels( fgens, grels, List( trial, UnderlyingElement ) ) called from
> Attempt( gens ) called from
> FinIndexCyclicSubgroupGenerator( G, infinity ) called from
> Size( C ) called from
> ...
> Entering break read-eval-print loop ...
> you can 'quit;' to quit to outer loop, or
> you can 'return;' to continue
> brk> 
> 
> I've run this on two machines, with gap -0 2G, and get similar nonresults. 
> The machines are 3.2GHz with 4GB memory running Ubuntu 10.04. and 
> Gap 4.4.12 of 17-Dec-2008. 
> 
> Am I just making some silly error? Or should I run this on a much more 
> powerful machine?
> 
> Thanks, Kirill M
> 
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum