The projective special semi-linear group $P\Sigma L\left(n\,q\right)$ is the quotient of the special semi-linear group $\Sigma L\left(n\,q\right)$ by the center of $SL\left(n\,q\right)$ .

For a positive integer n and a power q of a prime, the ProjectiveSpecialSemilinearGroup( n, q ) command returns a permutation group isomorphic to the projective special semi-linear group  $P\Sigma L\left(n\,q\right)$ . Otherwise, a symbolic group is returned, with which Maple can do some limited computations.

If q is a prime, then $P\Sigma L\left(n\,q\right)$ and $PSL\left(n\,q\right)$ are the same.

The abbreviation PSigmaL( n, q ) is available as a synonym for ProjectiveSpecialSemilinearGroup( n, q ).

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

$G≔\mathrm{ProjectiveSpecialSemilinearGroup}\left(1\,27\right)$

$G≔\mathbf{P\Sigma L}\left(1\,27\right)$

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

$3$

$G≔\mathrm{PSigmaL}\left(2\,7\right)$

$G≔\mathbf{P\Sigma L}\left(2\,7\right)$

$\mathrm{AreIsomorphic}\left(G\,\mathrm{PSL}\left(2\,7\right)\right)$

$\mathrm{true}$

$G≔\mathrm{PSigmaL}\left(2\,9\right)$

$G≔\mathbf{P\Sigma L}\left(2\,9\right)$

$\mathrm{AreIsomorphic}\left(G\,\mathrm{Symm}\left(6\right)\right)$

$\mathrm{true}$

$G≔\mathrm{PSigmaL}\left(4\,4\right)$

$G≔\mathbf{P\Sigma L}\left(4\,4\right)$

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

$\mathrm{true}$

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

$2$