By "constructive" I mean something that would go through in <a href="http://en.wikipedia.org/wiki/Constructive_set_theory">CZF</a> for example.

In practice, an answer to the following question will probably yield an answer (and if it fails to, it will probably be for an interesting reason)

I call a PER-Group a subset G of natural numbers, and equivalence relation R on G, with multiplication and inverse operations as partial computable functions, totally defined over G, and respecting R. 

Note G and R need not even be c.e. For instance, addition over the computable reals is computable, even though the set of codes for computable reals is not c.e., nor is equality of two computable reals. Of course that example is abelian, and the proof that every abelian group monomorphism is normal is constructive. I am interested in the non-abelian case.

> Is every PER-group inclusion the equaliser of two PER-group homomorphisms?