PlanetMath: normal is not transitive

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normal is not transitive

(Definition)

The phrase “normal is not transitive” can be used as a mnemonic for two statements.

The first is: “The relation `is a normal subgroup of' is not transitive.” This means that, if $H \triangleleft N \triangleleft G$ , it does not follow that $H \triangleleft G$ . See normality of subgroups is not transitive for more details.

The second is: “The relation `is a normal extension of' is not transitive.” This means that, if and are normal extensions, it does not follow that is normal. See example of normal extension for more details.

"normal is not transitive" is owned by Wkbj79.

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See Also: example of normal extension, normality of subgroups is not transitive

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Cross-references: example of normal extension, normal extensions, normality of subgroups is not transitive, mnemonic
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This is version 6 of normal is not transitive, born on 2006-06-15, modified 2007-05-21.
Object id is 8043, canonical name is NormalIsNotTransitive.
Accessed 934 times total.

Classification:

AMS MSC:	12F10 (Field theory and polynomials :: Field extensions :: Separable extensions, Galois theory)
	20A05 (Group theory and generalizations :: Foundations :: Axiomatics and elementary properties)

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