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Algebra and Discrete Mathematics, 2020, Volume 30, Issue 2, Pages 239–253
DOI: https://doi.org/10.12958/adm1264 (Mi adm779) 		 
RESEARCH ARTICLE

Groups whose lattices of normal subgroups are factorial

A. Rajhiab

a Mathematics Department, Faculty of Sciences and Humanities in Dawadmi, Shaqra University, 11911, Saudi Arabia
b Quantitative Methods Department, Higher business School, University of Manouba, Manouba 2010, Tunisia
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DOI: https://doi.org/10.12958/adm1264
Abstract: 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.
Received: 09.10.2018
Revised: 08.12.2020
Bibliographic databases:
Document Type: Article
MSC: 20E99, 06B99
Language: English
Citation: A. Rajhi, “Groups whose lattices of normal subgroups are factorial”, Algebra Discrete Math., 30:2 (2020), 239–253
Citation in format AMSBIB
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\by A.~Rajhi
\paper Groups whose lattices of normal subgroups are~factorial
\jour Algebra Discrete Math.
\yr 2020
\vol 30
\issue 2
\pages 239--253
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