A map φ: G → H with φ(ab) = φ(a)φ(b). Kernel = φ⁻¹(e_H) is a normal subgroup of G; image is a subgroup of H. First isomorphism theorem: G/ker(φ) ≅ im(φ).
A map φ: G → H with φ(ab) = φ(a)φ(b). Kernel = φ⁻¹(e_H) is a normal subgroup of G; image is a subgroup of H. First isomorphism theorem: G/ker(φ) ≅ im(φ).