  We say that a finite almost simple $G$ with socle $S$ is admissible (with
respect to the spectrum) if $G$ and $S$ have the same sets of orders of
elements. Let $L$ be a finite simple linear or unitary group of dimension at
least three over a field of odd characteristic. We describe admissible almost
simple groups with socle $L$. Also we calculate the orders of elements of the
coset $L\tau$, where $\tau$ is the inverse-transpose automorphism of $L$.
