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

# Group Kernel

## See also

Cokernel, Group Homomorphism, Module Kernel, Ring Kernel
*This entry contributed by Margherita
Barile*

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## Cite this as:

Barile, Margherita. "Group Kernel." From *MathWorld*--A Wolfram Web Resource, created by Eric
W. Weisstein. https://mathworld.wolfram.com/GroupKernel.html