@article{Endimioni_2004, title={Hopficity and Co-Hopficity in Soluble Groups}, volume={56}, url={https://umj.imath.kiev.ua/index.php/umj/article/view/3846}, abstractNote={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.}, number={10}, journal={Ukrainsâ€™kyi Matematychnyi Zhurnal}, author={Endimioni, G.}, year={2004}, month={Oct.}, pages={1335-1341} }