What question did this study set out to answer?

To determine the discrete cocompact subgroups of generic filiform nilpotent Lie groups up to isomorphism.

March 29, 2026Open Access

Discrete Cocompact Subgroups of the Generic Filiform Nilpotent Lie Groups

Key Points

To determine the discrete cocompact subgroups of generic filiform nilpotent Lie groups up to isomorphism.
Analyzed the structure of generic filiform nilpotent Lie groups in arbitrary dimensions.
Identified and classified discrete cocompact subgroups.
Provided explicit examples for four and five dimensional generic filiform nilpotent Lie groups.
Explicitly determined discrete cocompact subgroups for the four-dimensional group.
Explicitly determined discrete cocompact subgroups for the five-dimensional group.

Abstract

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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