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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.
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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.
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