Unipotent automorphism: Difference between revisions

Latest revision as of 00:04, 20 July 2009

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 $σ \in A u t (G)$ and $g \in G$ , denote by $[g, σ]$ the element $g^{- 1} σ (g)$ . Then $σ$ is said to be unipotent of class $n$ if for any $g \in G$ :

$[[[\dots [g, σ], σ], \dots] = e$

with $σ$ written $n$ times.

@@ Line 3: / Line 3: @@
 ==Definition==
-===Definition with symbols===
+===Definition with symbols (right action convention)===
-Let <math>G</math> be a group. For <math>\sigma \in Aut(G)</math> and <math>g \in G</math>, denote by <math>[g,\sigma]</math> the element <math>g^{-1}\sigma(g)</math>. Then <math>\sigma</math> is said to be unipotent of class <math>n</math> if for any <math>g \in G</math>:
+Let <math>G</math> be a group. For <math>\sigma \in \operatorname{Aut}(G)</math> and <math>g \in G</math>, denote by <math>[g,\sigma]</math> the element <math>g^{-1}\sigma(g)</math>. Then <math>\sigma</math> is said to be unipotent of class <math>n</math> if for any <math>g \in G</math>:
 <math>[[[\ldots[g,\sigma],\sigma],\ldots] = e</math>
+with <math>\sigma</math> written <math>n</math> times.