Geodesic
Groups whose lattices of normal subgroups are~factorial
Algebra and discrete mathematics, Tome 30 (2020) no. 2, pp. 239-253

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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.
Keywords: lattice of normal subgroups, semilattices, idempotent monoids, partial monoids. 
@article{ADM_2020_30_2_a7,
     author = {A. Rajhi},
     title = {Groups whose lattices of normal subgroups are~factorial},
     journal = {Algebra and discrete mathematics},
     pages = {239--253},
     publisher = {mathdoc},
     volume = {30},
     number = {2},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2020_30_2_a7/}
}
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A. Rajhi. Groups whose lattices of normal subgroups are~factorial. Algebra and discrete mathematics, Tome 30 (2020) no. 2, pp. 239-253. http://geodesic.mathdoc.fr/item/ADM_2020_30_2_a7/