[GAP Forum] Generating Set for Special Linear Groups

[Piyush garg]

Dear GAP Forum,

I am very tahnkful to Peter, Stefan and Steve for helping me out.
Now I am able to do this through GeneratorsOfGroup and SmallGeneratingSet ,
but I am still getting the error message for MinimalGeneratingSet (thats ok,
i will keep it on hold for moment).

I have two more doubts :
##    How to get the matrices from the output generated by GeneratorsOfGroup
for the Special Linear Group;  like for SL(2,17) :
s:=SL(2,17);
gens:=GeneratorsOfGroup(s);
[ [ [ Z(17), 0*Z(17)], [ 0*Z(17), Z(17)^15 ] ],
  [ [ Z(17)^8, Z(17)^0], [Z(17)^8, 0*Z(17)] ] ]

this is the output we are getting, now hwo to get the matrices from it which
can generate the whole set of SL(2,17) ??  (with the elements' values from 0
to 16.)

##    How can we store this output of matrices in a file and make use of
them in Matlab program ??
like storing the matrices now generated in a 3d-array and then later using
them in Matlab.

Thank you again for helping me out.

Regards,
Piyush Garg.


On Mon, Jun 6, 2011 at 7:51 PM, Stephen Linton <sal at cs.st-andrews.ac.uk>wrote:

> 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