Let ρ:GK be a group homomorphismMathworldPlanetmath. The preimageMathworldPlanetmath of the codomain identity elementMathworldPlanetmath eKK forms a subgroupMathworldPlanetmathPlanetmath of the domain G, called the kernel of the homomorphismMathworldPlanetmathPlanetmathPlanetmathPlanetmathPlanetmathPlanetmath;


The kernel is a normal subgroupMathworldPlanetmath. It is the trivial subgroup if and only if ρ is a monomorphismMathworldPlanetmathPlanetmath.

Title kernel
Canonical name Kernel
Date of creation 2013-03-22 11:58:24
Last modified on 2013-03-22 11:58:24
Owner rmilson (146)
Last modified by rmilson (146)
Numerical id 14
Author rmilson (146)
Entry type Definition
Classification msc 20A05
Synonym kernel of a group homomorphism
Related topic GroupHomomorphism
Related topic Kernel
Related topic AHomomorphismIsInjectiveIffTheKernelIsTrivial