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 > > > > _______________________________________________ > > Forum mailing list > > Forum@mail.gap-system.org > > http://mail.gap-system.org/mailman/listinfo/forum _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
