Let \(G\) and \(H\) be groups . A function \(f\colon G\to H\) is called homomorphism if it preserves multiplication, i.e. \(f(gh)=f(g)f(h)\).
Remarks
- \(f(1_G)=1_H\)
- \(f(g^{-1})=f(g)^{-1}\)
Let \(G\) and \(H\) be groups . A function \(f\colon G\to H\) is called homomorphism if it preserves multiplication, i.e. \(f(gh)=f(g)f(h)\).