A normal subgroup
of a group is a subgroup satisfying
for every element .
This condition is written (Arfken 1985, p. 242; Scott 1987, p. 25).
Normal subgroups are also called invariant subgroups or self-conjugate subgroups
(Arfken 1985, p. 242).
All subgroups of Abelian groups are normal (Arfken
1985, p. 242).
of a group 
is a subgroup satisfying
.
This condition is written 
(Arfken 1985, p. 242; Scott 1987, p. 25).
Normal subgroups are also called invariant subgroups or self-conjugate subgroups
(Arfken 1985, p. 242).
