ThmDex – An index of mathematical definitions, results, and conjectures.
▼ Set of symbols
▼ Alphabet
▼ Deduction system
▼ Theory
▼ Zermelo-Fraenkel set theory
▼ Set
▼ Binary cartesian set product
▼ Binary relation
▼ Map
▼ Operation
▼ N-operation
▼ Binary operation
▼ Enclosed binary operation
▼ Groupoid
▼ Groupoid homomorphism
▼ Semigroup homomorphism
▼ Monoid homomorphism
Definition D948
Group homomorphism
Formulation 0
Let $G$ and $H$ each be a D22: Group.
A D18: Map $f : G \to H$ is a group homomorphism from $G$ to $H$ if and only if \begin{equation} \forall \, x, y \in G : f(x y) = f(x) f(y) \end{equation}
Children
▶ D950: Ring homomorphism