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?

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

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