Geodesic
The Number of Sides of a Parallelogram
Discrete mathematics & theoretical computer science, Tome 3 (1998-1999) no. 2.

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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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     title = {The {Number} of {Sides} of a {Parallelogram}},
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Falbel, Elisha; Koseleff, Pierre-Vincent. The Number of Sides of a Parallelogram. Discrete mathematics & theoretical computer science, Tome 3 (1998-1999) no. 2. doi : 10.46298/dmtcs.251. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.251/

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