Grechkoseeva Mariya

On orders of elements of finite almost simple groups with linear or unitary socle

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 $Lτ$, where $τ$ is the inverse-transpose automorphism of $L$.