Projectively universal countable metrizable groups

Abstract

We prove that there exists a countable metrizable topological group $G$ such that every countable metrizable group is isomorphic to a quotient of $G$. The completion $H$ of $G$ is a Polish group such that every Polish group is isomorphic to a quotient of $H$.

7 pages, latex 2e. The proof at the end of Section 3 has been expanded, minor inaccuracies fixed