Convention:Group action on left
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.
By default (i.e. unless stated explicitly otherwise) group actions on sets are on the left.
This relates to the following other conventions:
- the convention for function composition: the convention for group action is compatible with the convention for composing functions.
- the convention for conjugation: The convention for conjugation is chosen such that we get a group action on the left.
The exception is in advanced purely group-theoretic areas, where group actions are conventionally done on the right, with right exponentation notation. In general, definitions are given in a way that does not use either a left/right convention. In cases where the definition has to use notation that requires choosing between left and right action, the definition is given using both conventions.
The reason why the convention does not ultimately matter follows from the fact that every group is naturally isomorphic to its opposite group.