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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
, it does not follow that
. 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 and are normal extensions, it does not follow that is normal. See example of normal extension for more details.
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