Let 
denote the group
of all invertible maps 
and let 
be any group. A homomorphism 
is called an action
of 
on 
. 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 Web Resource. https://mathworld.wolfram.com/Action.html