[GAP Forum] free nilpotent p-groups?

[Leonard Soicher]

Or, is the problem in computing in your group after it is constructed
by a PQuotient program?  Here in particular, for p-groups with p
large, you should be making use of a "Deep Thought" collector (see
C.R. Leedham-Green and L.H. Soicher,  Symbolic collection using Deep
Thought,  London Math. Soc. J. Comput. Math. 1 (1998), 9-24).

Regards,
Leonard

On Tue, Nov 21, 2006 at 02:10:15PM +0000, Leonard Soicher wrote:
> 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
> > EPFL SB SMA IMB MAD         \    Téléphone: +41 21-6935458
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