# Every group is a quotient of a residually finite group

From Groupprops

This article gives the statement, and possibly proof, of a group property (i.e., residually finite group) satisfying a group metaproperty (i.e., quotient-universal group property)

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## Statement

Let be a group. Then, there exists a residually finite group and a normal subgroup of such that is isomorphic to the quotient group .

## Facts used

## Proof

The proof follows directly by combining Facts (1) and (2). More explicitly, we choose the residually finite group to be the free group arising in the proof of Fact (1).