Galois is not transitive

The phrase “Galois is not transitive” is a mnemonic for the statement “The relation ‘is a Galois extension of’ is not transitive.” This means that, if $K/F$ and $L/K$ are Galois extensions (http://planetmath.org/GaloisExtension), it does not follow that $L/F$ is Galois. This follows immediately from the fact that normal is not transitive. See example of normal extension for more details.