Group Kernel

The kernel of a group homomorphism f:G-->G^' is the set of all elements of G which are mapped to the identity element of G^'. The kernel is a normal subgroup of G, and always contains the identity element of G. It is reduced to the identity element iff f is injective.

See also

Cokernel, Group Homomorphism, Module Kernel, Ring Kernel

This entry contributed by Margherita Barile

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Barile, Margherita. "Group Kernel." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein.

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