An action of a group 
on 
is a homomorphism 
,
where 
is the group
of all invertible maps 
.
Therefore, 
satisfies
1. For each 
, 
is a map 
.
2. 
.
3. 
, where 
is the group identity in 
.
4. 
.
Action
See also
Cascade, Flow, Group Action, Semidirect Product, SemiflowExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Action." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Action.html