A group set is a set whose elements are acted on by a group. If the group 
acts on the set 
, then 
is called a G-set.
Let 
be a group and let 
be a G-set. Then for every element
of 
and every element 
of 
,
an element 
of 
is associated in such a way that 
, where 
is the identity element
of 
and such that 
for every pair of elements 
.
The multiplication of elements of 
by elements of 
described above is called a left 
-action, since the elements of 
are multiplied on the left. For this reason, 
is sometimes called a left 
-set. Right 
-sets are defined analogously to left 
-sets except that multiplication by elements of 
is now performed to the right of elements of 
.
