# [GAP Forum] New features for the Polycyclic package ;

Claude Archer carcher at ulb.ac.be
Fri Apr 23 11:48:21 BST 2004

```Dear Bettina, dear forum members ,

I will reformulate question 4 on non prime pcgs with the polycyclic package.

suppose l:=[g1,g2,g3] is a pcgs for G. The it is possible to build a new Pc group (newG )
whose pcgs is l using :
newpcgs:=PcgsByPcSequence(FamilyObj(l[1]), l );
newG:=PcGroupWithPcgs(newpcgs); # at the moment Gap only accepts it if l is a prime pcgs

How to do that on a pcp group with an arbitrary non prime pcgs l
(in order to build a new pcp group) ?

> 2) > I would like to compute the second cohomology groups Z2(G,A) and B2(G,A)
> of an arbitrary finitely generated abelian group A.

Answer : you can use a G-invariant series through A
with elementary abelian factors and do induction along such a series.

Yes i understand that but the problem is that after some steps you get too many extensions
of groups A' that are not isomorphic to A even if they have the same type of G-invariant series.

That is why i was looking for implemeting a  direct method using linear equations on integer (cfr Holt)

Regards
Claude

```