A group action 
is effective if there are no trivial actions.
In particular, this means that there is no element of the group
(besides the identity element) which does nothing,
leaving every point where it is. This can be expressed as 
, where 
is the isotropy group
at 
and 
is the identity of 
.
It is possible for a Lie group 
to have an effective action on a smaller dimensional space
. However,
 |
is finite, and is called the degree of symmetry of 
.
