The special unitary group $SU\left(n\,q\right)$ is the set of all n x n matrices over the field with $q^2$ elements whose determinant is $1$ and respect a fixed nondegenerate sesquilinear form.

The SpecialUnitaryGroup( n, q ) command returns a permutation group isomorphic to the special unitary group  $SU\left(n\,q\right)$ .

Note that for n=2 the groups $SU\left(n\,q\right)$ and $SL\left(n\,q\right)$ are isomorphic so the latter is returned in this case.

The ranges for $n$ and $q$ are as follows:

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

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

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

$G≔\mathrm{SpecialUnitaryGroup}\left(3\,2\right)$

$G≔\mathbf{SU}\left(3\,2\right)$

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

$\left[\left(2\,3\,5\,9\right)\left(4\,7\,13\,22\right)\left(6\,11\,19\,26\right)\left(8\,15\,17\,20\right)\left(10\,18\,25\,24\right)\left(12\,21\,27\,23\right)\,\left(1\,2\,4\,8\,16\,24\,21\,7\,14\,11\,20\,27\right)\left(3\,6\,12\,5\,10\,9\,17\,18\,19\,25\,22\,26\right)\left(13\,23\,15\right)\right]$

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

$\mathrm{true}$

$\mathrm{GroupOrder}\left(\mathrm{SpecialUnitaryGroup}\left(4\,2\right)\right)$

$25920$

$G≔\mathrm{SpecialUnitaryGroup}\left(2\,23\right)$

$G≔\mathbf{SL}\left(2\,23\right)$

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

$27$

$\mathrm{GroupOrder}\left(\mathrm{SpecialUnitaryGroup}\left(3\,q\right)\right)$

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

$\mathrm{MinPermRepDegree}\left(\mathrm{SpecialUnitaryGroup}\left(3\,5\right)\right)$

$378$

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

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

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