In
abstract algebra, a
normal subgroup is a
subgroup which is invariant under
conjugation by members of the group of which it is a part. In other words, a subgroup
H of a group
G is normal in
G if and only if
gH =
Hg for all
g in
G, i.e., the sets of left and right
cosets coincide. Normal subgroups (and
only normal subgroups) can be used to construct
quotient groups from a given
group.