Group theory and generalizations Foundations Concept
Kernel of a homomorphism
Summary
The kernel of a group homomorphism is the set of elements that it sends to the identity. It is a normal subgroup, and it measures how far the homomorphism is from being injective.
Where this leads
6 pages build on this one.
Further reading
- Web https://en.wikipedia.org/wiki/Kernel_(algebra), Group homomorphisms
About this page
| Tag | 0W88CEGQP1 |
|---|---|
| URI | m2://0W88CEGQP1 |
| Kind | concept |
| Writing | W1 stated |
| MSC | 20A05 |
| Same as |
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What this page needs for W2
- edge not_instance_of in: at least one non-example (0 of 1)
- edge specializes both: the more general notions and the special cases (0 of 1)
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What links here
Results about this
- The kernel is a normal subgroup
- First isomorphism theorem
- A homomorphism is injective iff its kernel is trivial
Definitions
Instances
- The special linear group is the kernel of the determinant
- The alternating group is the kernel of the sign