[GAP Forum] Getting a presentation of a p-lower central series quotient

[Alexander Hulpke]

Dear Forum, Dear Anthony Bak,

> I have a finitely presented group and I use the ANUPQ package to
> calculate the quotient groups of the p-lower central series.  I'd like
> to get the quotient group in terms of the free group I started with.

I believe you just want to use PqEpimorphism instead of Pq -- this will return the corresponding homomorphism connecting to the source group. [There also is the library function `EpimorphismPGroup' but it is less powerful than the external ANUPQ.]

Best,

   Alexander Hulpke



> For instance, just taking the case of the free group:
> 
> LoadPackage("anupq");
> F := FreeGroup("a","b","c","d");
> a := F.1;; b := F.2;; c := F.3; d := F.4;;
> QF2 := Pq(F : Prime := 2, ClassBound := 2);
> <pc group of size 16384 with 14 generators>
> 
> # Some Code here to describe the generators of QF2 as words in a,b,c,d
> 
> The same thing for a group G defined by G := F/R, QG2:=Pq(G : Prime :=
> 2, ClassBound := 2);
> 
> (Apologies if I'm missing some basic GAP concepts - this is the first
> calculation I"ve tried to do).
> 
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