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In this paper, we prove (global) $q$-Poincar\'e inequalities for probabilitymeasures on nilpotent Lie groups with filiform Lie algebra of any length. Theprobability measures under consideration have a density with respect to theHaar measure given as a function of a suitable homogeneous norm.

$q$-Poincar\'e inequalities on Carnot Groups with filiform type Lie algebra