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
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