Linear group twisted by automorphisms (awaiting review)

The group $\Gamma\mathrm{L} (n,q)$ is the semi-direct product of $\GL(n,q)$ with the group of field automorphisms $A = \Aut(\F_q / \F_p)$, acting $\GL(n,q)$ entry-wise. Similarly, $\Sigma \mathrm{L}(n,q)$ is the semi-direct product of $\SL(n,q)$ with $A$.

The projective linear groups twisted by automorphisms are $\PGammaL(n,q)$ and $\PSigmaL(n,q)$, the quotients of $\Gamma \mathrm{L}(n,q)$ and $\Sigma \mathrm{L}(n,q)$, respectively, by their subgroups of scalar matrices.