Agroup \( G \) is called **residually finite** if for every nontrivial element \( g \in G \) (i.e., \( g \neq e \), where \( e \) is the identity element of the group), there exists afinite group \( H \) and agroup homomorphism \( \varphi: G \to H \) such that \( \varphi(g) \neq \varphi(e) \).