**MSC:**- 54A20 Convergence in general topology (sequences, filters, limits, convergence spaces, etc.)
- 54A99 None of the above but in this section

resource for counterexamples. So the free commutative group over a

completely regular, non-normal topological space is an example of a

non-normal topological group. In this paper we construct the free

commutative convergence group ${\cal A}_c(X)$ over a Hausdorff convergence space $X$.

We show that it is a complete, Hausdorff convergence group and that $X$ can

be embedded as a closed subspace into ${\cal A}_c(X)$.