[GAP Forum] specail linear group recognization

[Peter Brooksbank]

Hello Ayan,

There is a better way to do this, but it does not seem to be  
implemented yet in GAP (at least it isn't on the somewhat dated  
version that I just tried). The function will eventually be

IsNaturalSL ( matgrp )

At present this function seems to be computing the order of the  
matrix group and comparing it to the order of SL. As with the method  
you tried, this is very slow, even over modest dimensions and field  
sizes. Does anyone know whether this function is likely to be  
upgraded in coming releases?

Best Regards,

Peter

On Dec 10, 2007, at 2:58 PM, Ayan Mahalanobis wrote:

> Hello Forum,
>
> I am trying to find out whether a set generates the special linear  
> group over a given finite field. In my quest I pick a set of  
> matrices and then generate the group by them using the Group  
> function. Then I issue the command group=SL(d,q), where d is the  
> degree of the matrix and the q is the finite field. But this is not  
> successful even for small d and q.
>
> So basically my question is: Is there a better way to check that a  
> given group ( given as a matrix group by generators) equals the  
> special linear group?
>
> Regards,
> Ayan
>
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum