Hopficity and Co-Hopficity in Soluble Groups

  • G. Endimioni


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.
How to Cite
Endimioni, G. “Hopficity and Co-Hopficity in Soluble Groups”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 56, no. 10, Oct. 2004, pp. 1335-41, https://umj.imath.kiev.ua/index.php/umj/article/view/3846.
Research articles