Relatively morphic submodules are defined and a new class of modules between morphic and Hopfian modules is singled out. Special care is given to the Abelian groups case.

It is proved that the commutator subgroup of the fundamental group of the complement of any plane affine irreducible Hurwitz curve (respectively, any plane affine irreducible pseudoholomorphic curve) is finitely presented. It is shown that there exists a pseudo-holomorphic curve (a Hurwitz curve) in CP whose fundamental group of the complement is not Hopfian and, respectively, this group is not...

In this article we prove that an isometric multiple HNN extension of a group satisfying the falsification by fellow traveler property is almost convex. As a corollary, Wise’s example of a CAT(0) non-Hopfian group is almost convex.