Galois is not transitiveGaloisIsNotTransitive2006-06-15 02:44:312007-05-30 05:25:35DefinitionGalois extension% this is the default PlanetMath preamble. as your knowledge
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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 \PMlinkname{Galois extensions}{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.