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Homenormal is not transitive

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# 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.

Related:

ExampleOfNormalExtension, NormalityOfSubgroupsIsNotTransitive

Major Section:

Reference

Type of Math Object:

Definition

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## Mathematics Subject Classification

20A05*no label found*12F10

*no label found*

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