Terminology: Name for an operator $T$ where $T^n = I$ I'm thinking specifically of a linear operator $T$, for example rotation by a rational multiple of $\pi$ where for some $n$,  $T^n = I$.
It occurs to me that this property could apply generally to mappings of various structures.
Is there a name for this property ?

In the context of groups, $T$ is said to have finite order or to be a torsion element. When $T$ is a linear operator on a vector space $V$, the group is the general linear group $GL(V)$ of automorphisms of $V$.
Therefore, a good name for "$T^n=I$" is "$T$ is a linear automorphism of finite order".
