normal is not transitive

The phrase “normal is not transitive” can be used as a mnemonic for two statements.

The first is: “The relationMathworldPlanetmathPlanetmath ‘is a normal subgroupMathworldPlanetmath of’ is not transitiveMathworldPlanetmathPlanetmathPlanetmathPlanetmathPlanetmath.” This means that, if HNG, it does not follow that HG. See normality of subgroups is not transitive for more details.

The second is: “The relation ‘is a normal extensionMathworldPlanetmath 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