Unipotent automorphism

From Groupprops
Jump to: navigation, search
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)
View other automorphism properties OR View other function properties


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.