# Semantic search

Conjugacy-separable implies residually finite, Every group is a quotient of a residually finite group, Finitely generated abelian implies residually finite, Finitely generated and residually finite implies Hopfian, Finitely generated not implies residually finite, Free implies residually finite, Residual finiteness is not quotient-closed, Residual finiteness is restricted direct product-closed, Residual finiteness is subgroup-closed, Residually finite and all homomorphisms to any finite group can be listed in finite time implies solvable word problem, Residually finite and finitely many homomorphisms to any finite group implies Hopfian, Residually finite not implies Hopfian, Residually finite not implies finitely generated