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Journal of Lie Theory 18 (2008), No. 1, 001--016
Copyright Heldermann Verlag 2008

Discrete Cocompact Subgroups of the Generic Filiform Nilpotent Lie Groups

Hatem Hamrouni
Department of Mathematics, Faculty of Sciences, Route Soukra, B. P. 802, 3018 Sfax, Tunisia

The discrete cocompact subgroups of the generic filiform nilpotent Lie group with an arbitrary dimension are determined up to isomorphism. We close this paper with two examples in which we determine explicitly the discrete cocompact subgroups of the four dimensional and the five dimensional generic filiform nilpotent Lie groups.

Keywords: Nilpotent Lie group, discrete subgroup, rational structure.

MSC: 22E25, 22E40, 22E27

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