# What is the name of this transformation's property?

I have a transformation $P$ with the following property:

$P^n = \mathbb{I}$

(the identity) for some specific $n>1$, and all $P^m \neq 1$ for $m \neq n$.

What is the name of the property of $P$? Cyclic transformations are subsets of this, but are there more general, names?

• If $P^n=1$ then $P^{2n}=1$, so you must mean for $1\le m\lt n$. – André Nicolas Dec 3 '15 at 20:19
• I guess you can call it a root of unity, or a periodic matrix that is invertible. (mathworld.wolfram.com/PeriodicMatrix.html) – s.harp Dec 3 '15 at 20:27
• I agree with s.harp. It is a n:th root of unity. Although there may be more names for it too. – mathreadler Dec 3 '15 at 20:35