The term * normal closure* is used in two senses in mathematics:

- In group theory, the
**normal closure**of a subset of a group is the smallest normal subgroup that contains the subset; see conjugate closure. - In field theory, the
**normal closure**of an algebraic extension*F*/*K*is an extension field*L*of*F*such that*L*/*K*is normal and*L*is minimal with this property. See normal extension.

### Other articles related to "closure, normal closure, normal":

Conjugate Closure

... In group theory, the conjugate

... In group theory, the conjugate

**closure**of a subset S of a group G is the subgroup of G generated by SG, i.e ... the**closure**of SG under the group operation, where SG is the conjugates of the elements of S SG = {g−1sgNormal Extension -

... there is some algebraic extension M of L such that M is a

**Normal Closure**... there is some algebraic extension M of L such that M is a

**normal**extension of K ... such that the only subfield of M which contains L and which is a**normal**extension of K is M itself ... This extension is called the**normal closure**of the extension L of K ...### Famous quotes containing the word normal:

“As blacks, we need not be afraid that encouraging moral development, a conscience and guilt will prevent social action. Black children without the ability to feel a *normal* amount of guilt will victimize their parents, relatives and community first. They are unlikely to be involved in social action to improve the black community. Their self-centered personalities will cause them to look out for themselves without concern for others, black or white.”

—James P. Comer (20th century)

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