Hopficity and Co-Hopficity in Soluble Groups - Endimioni, G. (Ukrains’kyi Matematychnyi Zhurnal, 2004)
We show that a soluble group satisfying the minimal condition for its normal subgroups is co-hopfian and that a torsion-free finitely generated soluble group of finite rank is hopfian. The latter property is a consequence of a stronger result: in a minimax soluble group, the kernel of an endomorphism is finite if and only if its image is of finite index in the group.