[GAP Forum] Generating Set for Special Linear Groups

[Stephen Linton]

Dear GAP Forum,

As Peter has already reported, if you simply want a generating set then GeneratorsOfGroup is the appropriate function.
As you will see from the documentation (try ?GeneratorsSmallest for instance), the functions you called: GeneratorsSmallest and MinimalGeneratingSet
make much stronger promises about the result, which GAP has to do much more work to achieve. 

An intermediate choice is SmallGeneratingSet, which tries heuristically to reduce the size of the set it returns, but makes no firm promises. 

The error message from MinimalGeneratingSet is confusing,  but, in fact GAP has no way to compute this function for general groups. In the next release you will get the rather more helpful error message:

Error, `MinimalGeneratingSet' currently assumes that the group must be solvable.
In general, try `SmallGeneratingSet' instead, which returns a generating
set that is small but not of guarateed smallest cardinality

It is also possible, looking at the error message that you have mixed up g and G. Remember that GAP is case-sensitive.

Yours 

	Steve Linton

On 6 Jun 2011, at 06:39, Piyush garg wrote:
> 
> 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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