[GAP Forum] Basic question, order of fpgroup

KCHM k.mackenzie at sheffield.ac.uk
Wed Jul 27 16:27:39 BST 2011


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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