Torsion-free groups with every proper homomorphic image an \(\bf N_1\)-group

• Date: 2018
• Main Author: Ercan, Selami
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2018
• Subjects: all subgroups subnormal; torsion-free group; locally nilpotent groups; homomorphic image; 20E15; 20F14
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/990
• Journal Title: Algebra and Discrete Mathematics

In this article it is proved that a torsion-free locally nilpotent groups with non-trivial Fitting subgroup and every proper homomorphic image an \(\bf N_{1}\)-group is an \(\bf N_{1}\)-group(and so it is nilpotent).