Groups whose lattices of normal subgroups are factorial
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.
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| Datum: | 2021 |
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| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Lugansk National Taras Shevchenko University
2021
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| Schlagworte: | |
| Online Zugang: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1264 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| Zusammenfassung: | 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. |
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