The projective general unitary group $PGU\left(n\,q\right)$ is the quotient of the general unitary group $GU\left(n\,q\right)$ by its center.

The ProjectiveGeneralUnitaryGroup( n, q ) command returns a permutation group isomorphic to the projective general unitary group of degree $n$ over the field with $q^2$ elements. In general, this is not a transitive representation.

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

If either or both of the arguments n and q are non-numeric, then a symbolic group representing the projective general unitary group is returned.

The command PGU( n, q ) is provided as an abbreviation.

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

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

$\mathrm{ProjectiveGeneralUnitaryGroup}\left(2\,13\right)$

$\mathbf{PGL}\left(2\,13\right)$

$G≔\mathrm{PGU}\left(4\,4\right)$

$G≔\mathbf{PGU}\left(4\,4\right)$

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

$1018368000$

$\mathrm{IsTransitive}\left(\mathrm{PGU}\left(3\,3\right)\right)$

$\mathrm{true}$

$\mathrm{IsPrimitive}\left(\mathrm{PGU}\left(3\,3\right)\right)$

$\mathrm{true}$

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

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

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

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

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