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Discrete Cocompact Subgroups of the Five-Dimensional Connected and Simply Connected Nilpotent Lie Groups
Symmetry, integrability and geometry: methods and applications, Tome 5 (2009) Cet article a éte moissonné depuis la source Math-Net.Ru

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The discrete cocompact subgroups of the five-dimensional connected, simply connected nilpotent Lie groups are determined up to isomorphism. Moreover, we prove if $G=N\times A$ is a connected, simply connected, nilpotent Lie group with an Abelian factor $A$, then every uniform subgroup of $G$ is the direct product of a uniform subgroup of $N$ and $\mathbb Z^r$ where $r=\dim A$.
Keywords: nilpotent Lie group; discrete subgroup; nil-manifold; rational structures, Smith normal form; Hermite normal form. 
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Amira Ghorbel; Hatem Hamrouni. Discrete Cocompact Subgroups of the Five-Dimensional Connected and Simply Connected Nilpotent Lie Groups. Symmetry, integrability and geometry: methods and applications, Tome 5 (2009). http://geodesic.mathdoc.fr/item/SIGMA_2009_5_a19/

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