Let $\mathcal{F}$ be a filed, $\mathcal{G}=GL(n,\mathcal{F})$, all n×n invertible matrices
on $\mathcal{F}$, What is $Aut(\mathcal{G})$ ?



the automorphism group  of  the general linear group GL(n,F) 
See Chapt.IV in the book


Dieudonné, J. A.
La géométrie des groupes classiques. Springer-Verlag (1971).


