In this paper, we give a systolic inequality for a quotient space of a Carnot group Γ\G with Popp's volume. Namely we show the existence of a positive constant C such that the systole of Γ\G is less than Cvol(Γ\G) 1 Q , where Q is the Hausdorff dimension. Moreover, the constant depends only on the dimension of the grading of the Lie algebra g = V i . To prove this fact, the scalar product on G introduced in the definition of Popp's volume plays a key role.

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In this paper, we give a systolic inequality for quotient spaces of Carnot groups Γ\G with Popp's volume. Namely we show the existence of a positive constant C > 0 such that the systole of Γ\G is less than Cvol(Γ\G) 1 Q , where Q is the Hausdorff dimension. Moreover the constant depends only on the dimension of grading of the Lie algebra g = Vi.

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