Groups whose lattices of normal subgroups are factorial

• Date: 2021
• Main Author: Rajhi, A.
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2021
• Subjects: lattice of normal subgroups; semilattices; idempotent monoids; partial monoids; 20E99; 06B99
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1264
• Journal Title: Algebra and Discrete Mathematics

We prove that the groups \(G\) for which the lattice of normal subgroups \(\mathcal{N}(G)\) is factorial are exactly the UND-groups, that is the groups for which every normal subgroup have a unique normal complement, with finite length.