This analysis identifies discrete cocompact subgroups in generic filiform nilpotent Lie groups, suggesting new insights into their structure.
The discrete cocompact subgroups of the generic liform 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 ve dimensional generic liform nilpotent Lie groups.
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H. Hamrouni (2008) studied this question.