Hopficity and Co-Hopficity in Soluble Groups

• Date: 2004
• Main Authors: Endimioni, G., Ендиміоні, Г.
• Format: Article
• Language: English
• Published: Institute of Mathematics, NAS of Ukraine 2004
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/3846
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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 endomorphis...