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 $H◁N◁G$, it does not follow that $H◁G$. 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.

Title	normal is not transitive
Canonical name	NormalIsNotTransitive
Date of creation	2013-03-22 16:00:34
Last modified on	2013-03-22 16:00:34
Owner	Wkbj79 (1863)
Last modified by	Wkbj79 (1863)
Numerical id	9
Author	Wkbj79 (1863)
Entry type	Definition
Classification	msc 20A05
Classification	msc 12F10
Related topic	ExampleOfNormalExtension
Related topic	NormalityOfSubgroupsIsNotTransitive