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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 cosetL  ⁢  τ{L\tau}   , where τ is the inverse-transpose automorphism of  L .

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