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 aH = Ha for all a in G (see coset). Normal subgroups (and only normal subgroups) can be used to construct quotient groups from a given group.
Évariste Galois was the first to realize the importance of the existence of normal subgroups.
Read more about Normal Subgroup: Definitions, Examples, Properties, Normal Subgroups and Homomorphisms
Famous quotes containing the word normal:
“I don’t mind saying in advance that in my opinion jealousy is normal and healthy. Jealousy arises out of the fact that children love. If they have no capacity to love, then they don’t show jealousy.”
—D.W. Winnicott (20th century)