  We introduce the ozone group of a noncommutative algebra $A$, defined as the
group of automorphisms of $A$ which fix every element of its center. In order
to initiate the study of ozone groups, we study PI skew polynomial rings, which
have long proved to be a fertile testing ground in noncommutative algebra.
Using the ozone group and other invariants defined herein, we give explicit
conditions for the center of a PI skew polynomial to be Gorenstein (resp.
regular) in low dimension.
