[GAP Forum] Generating Set for Special Linear Groups

[Peter Brooksbank]

Dear Piyush,

I am not sure why this creates an error in GAP - perhaps someone else can
speak to that - but if all you want is a generating set for SL(n,q) you can
do the following:

G := SL (2, 13);
gens := GeneratorsOfGroup (G);

This will return the generators that GAP uses to construct the group G. For
the groups SL(n,q) my guess is that the list returned will  always be the
smallest possible (namely 2) if that is important to you.

Best,

Peter

On Mon, Jun 6, 2011 at 5:39 PM, Piyush garg <pgarg1990 at gmail.com> wrote:

> hii,
>
> I am using GAP for the very first time and facing problem in computing the
> generating set for the Special Linear Groups : SL(n,q) , defined over the
> finite fields.
>
> I have to find the generating set for the Special Linear group with given
> values of 'n' and 'q'.
> I was to able to do this for SL(2,13) by using
> g:=SL(2,13);
> GeneratorsSmallest(g);
>
> but when i made use of MinimalGeneratingSet(g); it showed an error :
>
> Error, no method found! For debugging hints type ?Recovery from
> NoMethodFound
> Error, no 2nd choice method found for `IndependentGeneratorsOfAbelianGroup'
> o
> n 1 arguments called from
> IndependentGeneratorsOfAbelianGroup( G ) called from
> <function>( <arguments> ) called from read-eval-loop
> Entering break read-eval-print loop ...
> you can 'quit;' to quit to outer loop, or
> you can 'return;' to continue
>
> and on using SmallGeneratingSet(g); it showed the following error :
>
> Variable : <debug-variable-1024-2> must have a value
>
> Can anyone please help out with the Minimal Generating Set thing and how to
> remove the error.
>
> Thanking you,
> Piyush garg.
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