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 KernelThis entry contributed by Margherita Barile
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Cite this as:
Weisstein, Eric W., with contributions by Margherita Barile. "Group Kernel." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/GroupKernel.html