High Quality Content by WIKIPEDIA articles! In the mathematical field of group theory, a group G is residually finite or finitely approximable if for every nontrivial element g in G there is a homomorphism h from G to a finite group.Examples of groups that are residually finite are finite groups, free groups, finitely generated nilpotent groups, polycyclic-by-finite groups, and fundamental groups of 3-manifolds. Subgroups of residually finite groups are residually finite, and direct products of residually finite groups are residually finite. Any inverse limit of residually finite groups is residually finite. In particular, all profinite groups are residually finite.

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