[GAP Forum] Basic question, order of fpgroup

[Vipul Naik]

As you may already know, the presentation I've given is the Coxeter
presentation for the symmetric group.

Vipul

* Quoting Vipul Naik who at 2011-07-27 10:45:42+0000 (Wed) wrote
> 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
> > 
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