[GAP Forum] Generators of Factor Groups

[Dmitrii Pasechnik]

Dear Minghui Liu,
On Tue, Mar 11, 2014 at 12:23:32PM +0800, Minghui Liu wrote:
> I am trying to find generators of a factor group. I have input dozens
> of generators and relations and when I use the command
> 
> AbelianInvariants(F/relations);
Have you looked at 

SmithNormalFormIntegerMat
SmithNormalFormIntegerMatTransforms

The transformation to apply to your original generators should be
readable from the output of SmithNormalFormIntegerMatTransforms.

IMHO it would be nice to have a more explicit function for the task at
hand.

HTH,
Dima
> 
> the result was something like
> 
> 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 3, 3, 3, 4, 4, 5
> 
> (I have reduced the number of 0's for simplicity.)
> 
> My question is, the result shows that the Abelianization of
> F/relations is a direct sum of some Z's and some finite cyclic groups;
> how can I find an explicit set of generators? I am especially
> interested in how to find the elements of order 2, 3, 4, 5,
> respectively.
> 
> Any assistance will be greatly appreciated.
> 
> Minghui