Discrete Mathematics & Theoretical Computer Science, Vol 3, No 2 (1999)

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The Number of Sides of a Parallelogram

Elisha Falbel, Pierre-Vincent Koseleff


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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