Given a group with elements 
and 
, there must be an element 
which is a similarity
transformation of 
so 
and 
are conjugate with respect to 
. Conjugate elements have the following properties:
1. Every element is conjugate with itself.
2. If 
is conjugate with 
with respect to 
,
then 
is conjugate to 
with respect to 
.
3. If 
is conjugate with 
and 
,
then 
and 
are conjugate with each other.
