Canonical presentation of a group ($⟨G\mid \ker (F(G)\to G)⟩$)

The canonical presentation of a group uses one symbol for each group element and all words that evaluate to the identity element as relators. Evaluation is a surjective group homomorphism from the free group on the underlying set; the first isomorphism theorem proves that the resulting group presentation recovers the original group. Equivalently the multiplication-table relators $s_g{s}_h{s}_{gh}^{-1}$ normally generate its kernel: they reduce every word to the symbol for its value. ^[ref]