Group theory and generalizations Foundations Concept
Group homomorphism
Summary
A group homomorphism is a map between groups that preserves the group operation. It is the basic way to compare two groups.
Where this leads
33 pages build on this one.
- Graph of groups
- Category of groups
- Full and faithful functors
- Hopfian group
- Free product
- Category of abelian groups
- Selmer group
- Ulam's stability problem
- Residually finite group
- Margulis superrigidity theorem
- Concrete category
- Jacobi sum
- Whitehead problem
- Character of an abelian group
- One-parameter subgroup
- Dirichlet character
- Group extension
- Functor
- Hecke character
- Zero morphism
- Galois representation
- Group representation
- Seifert–van Kampen theorem
- Wang's finiteness theorem
- Gauss sum
- Weil's local rigidity theorem
- Universal property
- Slice theorem
- Transfer homomorphism
- Continuous group homomorphism
- Calabi–Weil rigidity
- Morphism
- Grushko theorem
Further reading
- Web https://en.wikipedia.org/wiki/Group_homomorphism, lead section
About this page
| Tag | 0JYTG5K9Y4 |
|---|---|
| URI | m2://0JYTG5K9Y4 |
| Kind | concept |
| Writing | W2 usable |
| MSC | 20A05 |
| Same as |
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What this page needs for W3
- section Motivation: the question that the notion answers (0 of 1)
- section History: who introduced the notion and when (0 of 1)
- explanations for the audience (0 of 3)
- a person confirmed each agent-written section: rule P04 (0 of 1)
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What links here
Special cases
- Group isomorphism
- Transfer homomorphism
- Continuous group homomorphism
- Additive function
- One-parameter subgroup
Definitions
Results about this
Instances
- Determinant as a group homomorphism
- The exponential map from the additive reals to the positive reals
- Reduction modulo n is a homomorphism
- Doubling on the integers is not an isomorphism
Used by
- Graph of groups
- Category of groups
- Full and faithful functors
- Hopfian group
- Free product
- Category of abelian groups
- Selmer group
- Ulam's stability problem
- Residually finite group
- Margulis superrigidity theorem
- Concrete category
- Jacobi sum
- Whitehead problem
- Character of an abelian group
- One-parameter subgroup
- Dirichlet character
- Group extension
- Functor
- Hecke character
- Zero morphism
- Galois representation
- Group representation
- Seifert–van Kampen theorem
- Gauss sum
- Weil's local rigidity theorem
- Universal property
- Transfer homomorphism
- Continuous group homomorphism
- Calabi–Weil rigidity
- Morphism
- Grushko theorem