normal is not transitive

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 $K/F$ and $L/K$ are normal extensions, it does not follow that $L/F$ is normal. See example of normal extension for more details.

单词	NormalIsNotTransitive
释义	normal is not transitive 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 $K/F$ and $L/K$ are normal extensions, it does not follow that $L/F$ is normal. See example of normal extension for more details.
随便看	Van der Waerden’s permanent conjecture VandiversConjecture Vandiver’s conjecture VanishAtInfinity vanish at infinity VanishingOfGradientInDomain vanishing of gradient in domain VanKampensTheorem VanKampensTheoremResult Van Kampen’s theorem Van Kampen’s theorem result varepsilonnet Variable variable VariableCategory variable category VariableGroupoid variable groupoid VariableNetworkTopology variable network topology VariableTopology variable topology Variance variance VariantOfCardanosDerivation