Math and science::Algebra::Aluffi

Groups. Group action.

Consider a group and a target object, such as a set. A group actions associate each group element with [what?] of a target object, such as a set.

Let $G$ be a group with operation $m_{G} : G \times G \to G$ , and let $A$ and object. A function $σ : G \to Auto (A)$ is a group action iff:

the identity of $G$ maps to the identity of $A$ .
either:
1. for any $g, h \in G$ , $σ (m_{G} (g, h)) =$ [ $? \circ ?$ ] [left-action]
2. for any $g, h \in G$ , $σ (m_{G} (g, h)) =$ [ $? \circ ?$ ] [right-action]

Why are there two types of actions?

30.06.2022