A group action 
is called faithful if there are no group
elements 
(except the identity element) such that 
for all 
. Equivalently, the map 
induces an injection of 
into the symmetric
group 
.
So 
can be identified with a permutation subgroup.
Most actions that arise naturally are faithful. An example of an action which is not faithful is the action 
of 
on 
, i.e., 
.
