[GAP Forum] free nilpotent p-groups?

[Leonard Soicher]

Dear Laurent, 

It looks to me like you should be using a PQuotient program
that makes use of a "Deep Thought" collector. I doubt this is
the case with the anupq and don't know whether it is the case with 
GAP's `PQuotient' function, which runs very fast for your example:

gap> p := 1201;
1201
gap> r := 3;
3
gap> n := 4;
4
gap> F := FreeGroup(r);
<free group on the generators [ f1, f2, f3 ]>
gap> F := F / List(GeneratorsOfGroup(F),g->g^p);
<fp group on the generators [ f1, f2, f3 ]>
gap> PQuotient(F,p,n+1);
<1201-quotient system of 1201-class 5 with 80 generators>
gap>

Best wishes,
Leonard

On Fri, Nov 17, 2006 at 05:02:34PM +0100, Laurent Bartholdi wrote:
> dear forum,
> i'm a bit surprised by the performance of calculations in free
> nilpotent p-groups:
> in the following code, computation takes forever. if i replace p by a
> smaller prime, like 601, it's sluggish, while for really small primes
> it's blindingly fast.
> i was under the impression that computational time should scale
> logarithmically in p. can anybody help me out?
> 
> LoadPackage("anupq");
> p := 1201;
> r := 3;
> n := 4;
> F := FreeGroup(r);
> F := F / List(GeneratorsOfGroup(F),g->g^p);
> F := Pq(F : Prime := p, ClassBound := n+1);
> Print("alive\n");
> Print("F1^-1*F3=",F.1^-1*F.3,"\n");
> Print("F3^-1*F1=",F.3^-1*F.1,"\n (never reached!)");
> 
> -- 
> Laurent Bartholdi          \  laurent.bartholdi<at>gmail<dot>com
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