The special semi-linear group $\Sigma L\left(n\,q\right)$ is the set of all semi-linear transformations of an $n$-dimensional vector space $V$ over the field with $q$ elements whose linear part has determinant equal to $1$.

If n and q are positive integers, then the SpecialSemilinearGroup( n, q ) command returns a permutation group isomorphic to the special semi-linear group  $\Sigma L\left(n\,q\right)$ . Otherwise, a symbolic group is returned, for which Maple can do some limited computations.

The abbreviation SigmaL( n, q ) is available as a synonym for SpecialSemilinearGroup( n, q ).

$\mathrm{with}\left(\mathrm{GroupTheory}\right)\:$