The special linear group $SL\left(n\,q\right)$ is the set of all $n\times n$ nonsingular matrices over a finite field of size $q$ whose determinant is $1$.

The SpecialLinearGroup( n, q ) command returns a permutation group isomorphic to the special linear group $SL\left(n\,q\right)$ .

If either or both of the parameters n and q is non-numeric, then a symbolic group representing the indicated special linear group is returned.

In the Standard Worksheet interface, you can insert this group into a document or worksheet by using the Group Constructors palette.

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

$\mathrm{SpecialLinearGroup}\left(3\,2\right)$

$\mathbf{SL}\left(3\,2\right)$

$G≔\mathrm{SL}\left(2\,3\right)$

$G≔\mathbf{SL}\left(2\,3\right)$

$\mathrm{GroupOrder}\left(G\right)$

$24$

$\mathrm{GroupOrder}\left(\mathrm{SL}\left(4\,q\right)\right)$

$q^6\left(q^2-1\right)\left(q^3-1\right)\left(q^4-1\right)$

$G≔\mathrm{SL}\left(2\,5\right)$

$G≔\mathbf{SL}\left(2\,5\right)$

$\mathrm{IsPerfect}\left(G\right)$

$\mathrm{true}$

The GroupTheory[SpecialLinearGroup] command was introduced in Maple 17.

For more information on Maple 17 changes, see Updates in Maple 17.

The GroupTheory[SpecialLinearGroup] command was updated in Maple 2020.