Let 
be a subgroup of a group 
. The similarity transformation of 
by a fixed element 
in 
not in 
always gives a subgroup. If
 |
for every element 
in 
, then 
is said to be a normal subgroup of 
, written 
(Arfken 1985, p. 242; Scott 1987, p. 25). Normal subgroups are also known as invariant subgroups or self-conjugate subgroup (Arfken 1985, p. 242).
All subgroups of Abelian groups are normal (Arfken 1985, p. 242).
