Unipotent automorphism

This article defines an automorphism property, viz a property of group automorphisms. Hence, it also defines a function property (property of functions from a group to itself)
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Definition

Definition with symbols (right action convention)

Let $G$ be a group. For $\sigma \in \operatorname {Aut} (G)$ and $g\in G$, denote by $[g,\sigma ]$ the element $g^{-1}\sigma (g)$. Then $\sigma$ is said to be unipotent of class $n$ if for any $g\in G$:

$[[[\ldots [g,\sigma ],\sigma ],\ldots ]=e$

with $\sigma$ written $n$ times.