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The Number of Sides of a Parallelogram

Abstract : We define parallelograms of base a and b in a group. They appear as minimal relators in a presentation of a subgroup with generators a and b. In a Lie group they are realized as closed polygonal lines, with sides being orbits of left-invariant vector fields. We estimate the number of sides of parallelograms in a free nilpotent group and point out a relation to the rank of rational series.
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Elisha Falbel, Pierre-Vincent Koseleff. The Number of Sides of a Parallelogram. Discrete Mathematics and Theoretical Computer Science, DMTCS, 1999, Vol. 3 no. 2 (2), pp.33-42. ⟨10.46298/dmtcs.251⟩. ⟨hal-00958925⟩



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