 Residually finite group

A group $G$ is residually finite when every nonidentity $g\in G$ survives in some finite quotient: there are a finite group $Q$ and a homomorphism $\varphi :G\to Q$ with $\varphi (g)\ne 1$.

A group \( G \) 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 a finite group \( H \) and a group homomorphism \( \varphi: G \to H \) such that \( \varphi(g) \neq \varphi(e) \).