A subgroup 
of an original group 
has elements 
. Let 
be a fixed element of the original group 
which is not a member of 
. Then the transformation 
, (
, 2, ...) generates the so-called conjugate subgroup 
. If, for all 
, 
, then 
is a normal (also called
"self-conjugate" or "invariant") subgroup.
All subgroups of an Abelian group are normal.
