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.
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