Let 
be a group
and 
be a set. Then
is called a left 
-set if there exists a map 
such that
 |
for all 
and all 
. This is commonly written 
, so the above relation becomes
 |
The map 
is called a left 
-action on the set 
.
Right 
-sets and right 
-actions are defined analogously except elements of 
are multiplied by elements of 
to the right instead of to the left. Left 
-sets and right 
-sets are both called 
-sets for simplicity.
A 
-set is an example of a group
set, where 
is the group in question.
