# Convention:Conjugation

From Groupprops

This article is about a convention that is followed in this wiki. The aim is that every page on the wiki follows this convention unless explicitly stated otherwise on the page; however, in practice, this may not have been implemented

Also see switching between the left and right action conventions for background on the differences between various conventions.

If is a group and , the conjugation by is defined as the map:

This convention is compatible with the convention that a group action is on the left.

This notation is followed in a number of pages.

However, the notation is used to denote conjugation on the right. In other words . Thus, we have .

The latter notation is typically used in the theory of finite groups, when doing calculations involving conjugates and commutators. The primary advantage of this is that , which is convenient for results.

Because of the inherent left-right symmetry in groups, the main definitions remain the same whatever convention we choose. It is important to remember the conventions only when trying to follow a notation-heavy proof.