273 Homomorphism
A mapping from a domain to a codomain that is used to represent elements from one set in another set.
definition [d] (Homomorphism) From Pinter: if \(G\) and \(H\) are groups, a homomorphism from \(G\) to \(H\) is a function \(f: G \rightarrow H\) such that for any two elements \(a\) and \(b\) in \(G\),
- \(f(ab) = f(a)f(b)\) .
where
- \(G\) and \(H\) are groups.
- \(f\) is the homomorphism.
- \(a, b \in G\).
Note:
- If there exists a homomorphism from \(G\) onto \(H\), then \(H\) is a homomorphic image of \(G\).